James Lepowsky's Books

Vertex Operator Algebras and the Monster

By: Igor Frenkel,James Lepowsky,Arne Meurman

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Vertex Operator Algebras and the Monster

By: Igor Frenkel,James Lepowsky,Arne Meurman

This work is motivated by and develops connections between several branches of mathematics and physics--the theories of Lie algebras, finite groups and modular functions in mathematics, and string theory in physics. The first part of the book presents a new mathematical theory of vertex operator algebras, the algebraic counterpart of two-dimensional holomorphic conformal quantum field theory. The remaining part constructs the Monster finite simple group as the automorphism group of a very special vertex operator algebra, called the "moonshine module" because of its relevance to "monstrous moonshine.

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563

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Academic Press

Published Date

ISBN 10

0080874541

ISBN 13

9780080874548

Generalized Vertex Algebras and Relative Vertex Operators

By: Chongying Dong,James Lepowsky

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Generalized Vertex Algebras and Relative Vertex Operators

By: Chongying Dong,James Lepowsky

The rapidly-evolving theory of vertex operator algebras provides deep insight into many important algebraic structures. Vertex operator algebras can be viewed as "complex analogues" of both Lie algebras and associative algebras. The monograph is written in a n accessible and self-contained manner, with detailed proofs and with many examples interwoven through the axiomatic treatment as motivation and applications. It will be useful for research mathematicians and theoretical physicists working the such fields as representation theory and algebraic structure sand will provide the basis for a number of graduate courses and seminars on these and related topics.

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207

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Springer Science & Business Media

Published Date

ISBN 10

1461203538

ISBN 13

9781461203537

Functional Analysis on the Eve of the 21st Century

Volume I: In Honor of the Eightieth Birthday of I. M. Gelfand

By: Simon Gindikin,James Lepowsky,Robert Wilson

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Functional Analysis on the Eve of the 21st Century

Volume I: In Honor of the Eightieth Birthday of I. M. Gelfand

By: Simon Gindikin,James Lepowsky,Robert Wilson

A four-day conference, "Functional Analysis on the Eve of the Twenty First Century," was held at Rutgers University, New Brunswick, New Jersey, from October 24 to 27, 1993, in honor of the eightieth birthday of Professor Israel Moiseyevich Gelfand. He was born in Krasnye Okna, near Odessa, on September 2, 1913. Israel Gelfand has played a crucial role in the development of functional analysis during the last half-century. His work and his philosophy have in fact helped to shape our understanding of the term "functional analysis" itself, as has the celebrated journal Functional Analysis and Its Applications, which he edited for many years. Functional analysis appeared at the beginning of the century in the classic papers of Hilbert on integral operators. Its crucial aspect was the geometric interpretation of families of functions as infinite-dimensional spaces, and of op erators (particularly differential and integral operators) as infinite-dimensional analogues of matrices, directly leading to the geometrization of spectral theory. This view of functional analysis as infinite-dimensional geometry organically included many facets of nineteenth-century classical analysis, such as power series, Fourier series and integrals, and other integral transforms.

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312

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Springer Science & Business Media

Published Date

ISBN 10

1461225825

ISBN 13

9781461225829

Introduction to Vertex Operator Algebras and Their Representations

By: James Lepowsky,Haisheng Li

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Introduction to Vertex Operator Algebras and Their Representations

By: James Lepowsky,Haisheng Li

* Introduces the fundamental theory of vertex operator algebras and its basic techniques and examples. * Begins with a detailed presentation of the theoretical foundations and proceeds to a range of applications. * Includes a number of new, original results and brings fresh perspective to important works of many other researchers in algebra, lie theory, representation theory, string theory, quantum field theory, and other areas of math and physics.

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330

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Springer Science & Business Media

Published Date

ISBN 10

0817681868

ISBN 13

9780817681869

Cardinal Invariants On Boolean Algebras

By: James Donald Monk

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Cardinal Invariants On Boolean Algebras

By: James Donald Monk

This book is concerned with cardinal number valued functions defined for any Boolean algebra. Examples of such functions are independence, which assigns to each Boolean algebra the supremum of the cardinalities of its free subalgebras, and cellularity, which gives the supremum of cardinalities of sets of pairwise disjoint elements. Twenty-one such functions are studied in detail, and many more in passing. The questions considered are the behaviour of these functions under algebraic operations such as products, free products, ultraproducts, and their relationships to one another. Assuming familiarity with only the basics of Boolean algebras and set theory, through to simple infinite combinatorics and forcing, the book reviews current knowledge about these functions, giving complete proofs for most facts. A special feature of the book is the attention given to open problems, of which 97 are formulated. Based on Cardinal Functions on Boolean Algebras (1990) by the same author, the present work is nearly twice the size of the original work. It contains solutions to many of the open problems which are discussed in greater detail than before. Among the new topics considered are ultraproducts and FedorchukA-s theorem, and there is a more complete treatment of the cellularity of free products. Diagrams at the end of the book summarize the relationships between the functions for many important classes of Boolean algebras, including tree algebras and superatomic algebras. Review: "This book is an indispensable tool for anyone working in Boolean algebra, and is also recommended for set-theoretic topologists." - Zentralblatt MATH

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320

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Springer Science & Business Media

Published Date

ISBN 10

376435402X

ISBN 13

9783764354022

Representations of Semisimple Lie Algebras in the BGG Category O

By: James E. Humphreys

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Representations of Semisimple Lie Algebras in the BGG Category O

By: James E. Humphreys

This is the first textbook treatment of work leading to the landmark 1979 Kazhdan–Lusztig Conjecture on characters of simple highest weight modules for a semisimple Lie algebra g g over C C. The setting is the module category O O introduced by Bernstein–Gelfand–Gelfand, which includes all highest weight modules for g g such as Verma modules and finite dimensional simple modules. Analogues of this category have become influential in many areas of representation theory. Part I can be used as a text for independent study or for a mid-level one semester graduate course; it includes exercises and examples. The main prerequisite is familiarity with the structure theory of g g. Basic techniques in category O O such as BGG Reciprocity and Jantzen's translation functors are developed, culminating in an overview of the proof of the Kazhdan–Lusztig Conjecture (due to Beilinson–Bernstein and Brylinski–Kashiwara). The full proof however is beyond the scope of this book, requiring deep geometric methods: D D-modules and perverse sheaves on the flag variety. Part II introduces closely related topics important in current research: parabolic category O O, projective functors, tilting modules, twisting and completion functors, and Koszul duality theorem of Beilinson–Ginzburg–Soergel.

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289

Publisher

American Mathematical Soc.

Published Date

ISBN 10

1470463261

ISBN 13

9781470463267

The Origins Of Western Warfare

Militarism And Morality In The Ancient World

By: Doyne Dawson,James D Dawson

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The Origins Of Western Warfare

Militarism And Morality In The Ancient World

By: Doyne Dawson,James D Dawson

What is the source of the uniquely Western way of war, the persistent militarism that has made Europe the site of bloodshed throughout history and secured the dominance of the West over the rest of the world? The answer, Doyne Dawson persuasively argues in this groundbreaking new book, is to be found in the very bedrock of Western civilization: ancient Greece and Rome.The Origins of Western Warfare begins with an overview of primitive warfare, showing how the main motivations of prehistoric combat?revenge and honor?set the tone for Greek thinking about questions of war and morality. These ideas, especially as later developed by the Romans, ensured the emergence of a distinctive Western tradition of warfare: dynamic, aggressive, and devastatingly successful when turned against non-Western cultures.Dawson identifies key factors that led Western culture down this particular path. First, the Greeks argued that war could be justified as an instrument of human and divine justice, securing the social and cosmic order. Second, war was seen as a rational instrument of foreign policy. This, probably the most original contribution of the Greeks to military thought, was articulated as early as the fifth century b.c. Finally, Greek military thought was dominated by the principle of ?civic militarism,? in which the ideal state is based upon self-governing citizens trained and armed for war.The Roman version of civic militarism became thoroughly imperial in spirit, and in general, the Romans successfully modified these Greek ideas to serve their expansionist policies. At the end of antiquity, these traditions were passed on to medieval Europe, forming the basis for the just war doctrines of the Church. Later, in early modern Europe, they were fully revived, systematized, and given a basis in natural law?to the benefit of absolute monarchs. For centuries this neoclassical synthesis served the needs of European elites, and echoes of it are still heard in contemporary justifications for war.Providing a careful reconsideration of what the classical sources tell us about Western thinking on fundamental questions of war and peace, The Origins of Western Warfare makes a lasting contribution to our understanding of one of the most persistent and troubling aspects of Western culture.

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214

Publisher

Routledge

Published Date

ISBN 10

0429964633

ISBN 13

9780429964633

Lie Algebras, Vertex Operator Algebras and Their Applications

International Conference in Honor of James Lepowsky and Robert Wilson on Their Sixtieth Birthdays, May 17-21, 2005, North Carolina State University, Raleigh, North Carolina

By: Yi-Zhi Huang,Kailash C. Misra

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Lie Algebras, Vertex Operator Algebras and Their Applications

International Conference in Honor of James Lepowsky and Robert Wilson on Their Sixtieth Birthdays, May 17-21, 2005, North Carolina State University, Raleigh, North Carolina

By: Yi-Zhi Huang,Kailash C. Misra

The articles in this book are based on talks given at the international conference 'Lie algebras, vertex operator algebras and their applications'. The focus of the papers is mainly on Lie algebras, quantum groups, vertex operator algebras and their applications to number theory, combinatorics and conformal field theory.

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500

Publisher

American Mathematical Soc.

Published Date

ISBN 10

0821839861

ISBN 13

9780821839867

Rebranding Islam

Piety, Prosperity, and a Self-Help Guru

By: James Bourk Hoesterey

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Rebranding Islam

Piety, Prosperity, and a Self-Help Guru

By: James Bourk Hoesterey

Kyai Haji Abdullah Gymnastiar, known affectionately by Indonesians as "Aa Gym" (elder brother Gym), rose to fame via nationally televised sermons, best-selling books, and corporate training seminars. In Rebranding Islam James B. Hoesterey draws on two years' study of this charismatic leader and his message of Sufi ideas blended with Western pop psychology and management theory to examine new trends in the religious and economic desires of an aspiring middle class, the political predicaments bridging self and state, and the broader themes of religious authority, economic globalization, and the end(s) of political Islam. At Gymnastiar's Islamic school, television studios, and MQ Training complex, Hoesterey observed this charismatic preacher developing a training regimen called Manajemen Qolbu into Indonesia's leading self-help program via nationally televised sermons, best-selling books, and corporate training seminars. Hoesterey's analysis explains how Gymnastiar articulated and mobilized Islamic idioms of ethics and affect as a way to offer self-help solutions for Indonesia's moral, economic, and political problems. Hoesterey then shows how, after Aa Gym's fall, the former celebrity guru was eclipsed by other television preachers in what is the ever-changing mosaic of Islam in Indonesia. Although Rebranding Islam tells the story of one man, it is also an anthropology of Islamic psychology.

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293

Publisher

Stanford University Press

Published Date

ISBN 10

0804796386

ISBN 13

9780804796385

Planar Algebras in Braided Tensor Categories

By: André Gil Henriques,David Penneys,James E. Tener

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Planar Algebras in Braided Tensor Categories

By: André Gil Henriques,David Penneys,James E. Tener

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100

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American Mathematical Society

Published Date

ISBN 10

1470455404

ISBN 13

9781470455408

Introduction to Lie Algebras and Representation Theory

By: JAMES HUMPHREYS

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Introduction to Lie Algebras and Representation Theory

By: JAMES HUMPHREYS

This book is designed to introduce the reader to the theory of semisimple Lie algebras over an algebraically closed field of characteristic 0, with emphasis on representations. A good knowledge of linear algebra (including eigenvalues, bilinear forms, euclidean spaces, and tensor products of vector spaces) is presupposed, as well as some acquaintance with the methods of abstract algebra. The first four chapters might well be read by a bright undergraduate; however, the remaining three chapters are admittedly a little more demanding. Besides being useful in many parts of mathematics and physics, the theory of semisimple Lie algebras is inherently attractive, combining as it does a certain amount of depth and a satisfying degree of completeness in its basic results. Since Jacobson's book appeared a decade ago, improvements have been made even in the classical parts of the theory. I have tried to incor porate some of them here and to provide easier access to the subject for non-specialists. For the specialist, the following features should be noted: (I) The Jordan-Chevalley decomposition of linear transformations is emphasized, with "toral" subalgebras replacing the more traditional Cartan subalgebras in the semisimple case. (2) The conjugacy theorem for Cartan subalgebras is proved (following D. J. Winter and G. D. Mostow) by elementary Lie algebra methods, avoiding the use of algebraic geometry.

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198

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Springer Science & Business Media

Published Date

ISBN 10

0387900535

ISBN 13

9780387900537

Homotopy Theory and Its Applications

A Conference on Algebraic Topology in Honor of Samuel Gitler, August 9-13, 1993, Cocoyoc, Mexico

By: Alejandro Adem,R. James Milgram,Douglas C. Ravenel

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Homotopy Theory and Its Applications

A Conference on Algebraic Topology in Honor of Samuel Gitler, August 9-13, 1993, Cocoyoc, Mexico

By: Alejandro Adem,R. James Milgram,Douglas C. Ravenel

This book is the result of a conference held to examine developments in homotopy theory in honor of Samuel Gitler in July 1993 (Cocoyoc, Mexico). It includes several research papers and three expository papers on various topics in homotopy theory. The research papers discuss the following: BL application of homotopy theory to group theory BL fiber bundle theory BL homotopy theory The expository papers consider the following topics: BL the Atiyah-Jones conjecture (by C. Boyer) BL classifying spaces of finite groups (by J. Martino) BL instanton moduli spaces (by J. Milgram) Homotopy Theory and Its Applications offers a distinctive account of how homotopy theoretic methods can be applied to a variety of interesting problems.

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250

Publisher

American Mathematical Soc.

Published Date

ISBN 10

0821803050

ISBN 13

9780821803059

Converting California

Indians and Franciscans in the Missions

By: James A. Sandos

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Converting California

Indians and Franciscans in the Missions

By: James A. Sandos

This book is a compelling and balanced history of the California missions and their impact on the Indians they tried to convert. Focusing primarily on the religious conflict between the two groups, it sheds new light on the tensions, accomplishments, and limitations of the California mission experience. James A. Sandos, an eminent authority on the American West, traces the history of the Franciscan missions from the creation of the first one in 1769 until they were turned over to the public in 1836. Addressing such topics as the singular theology of the missions, the role of music in bonding Indians to Franciscan enterprises, the diseases caused by contact with the missions, and the Indian resistance to missionary activity, Sandos not only describes what happened in the California missions but offers a persuasive explanation for why it happened.

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272

Publisher

Yale University Press

Published Date

ISBN 10

0300129122

ISBN 13

9780300129120

Inside Interviewing

New Lenses, New Concerns

By: James Holstein,Jaber F. Gubrium

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Inside Interviewing

New Lenses, New Concerns

By: James Holstein,Jaber F. Gubrium

Inside Interviewing highlights the fluctuating and diverse moral worlds put into place during interview research when gender, race, culture and other subject positions are brought narratively to the foreground. It explores the 'facts', thoughts, feelings and perspectives of respondents and how this impacts on the research process.

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572

Publisher

SAGE

Published Date

ISBN 10

0761928510

ISBN 13

9780761928515

Handbook of Interview Research

Context and Method

By: Jaber F. Gubrium,James A. Holstein

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Handbook of Interview Research

Context and Method

By: Jaber F. Gubrium,James A. Holstein

Interviewing has become the window on the world of experience for both researchers and professionals. But as familiar as interviewing is now, its seemingly straightforward methodology raises more questions than ever. What is the interviewer's image of those who are being interviewed? Who is the interviewer in the eyes of the respondent? From where do interviewers obtain questions and respondents get the answers that they communicate in interviews? How do the institutional auspices of interviewing shape interview data? Drawing upon leading experts from a wide range of disciplines to address these and related questions, The Handbook of Interviewing offers a comprehensive examination of the interview at the cutting edge of information technology in the context of a challenging postmodern environment. Encyclopedic in its breadth, the Handbook provides extensive discussions of the conceptual and methodological issues surrounding interview practice in relation to forms of interviewing, new technology, diverse data gathering and analytic strategies, and the various ways interviewing relates to distinctive respondents. The Handbook is also a story that spins a particular tale that moves from the commonly recognized individual interview as an instrument for gathering data to reflections on the interview as an integral part of the information we gather about individuals and society.

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1423

Publisher

SAGE Publications

Published Date

ISBN 10

1483365891

ISBN 13

9781483365893

Function Estimates

Proceedings of a Conference Held July 28-August 3, 1985

By: James Stephen Marron

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Function Estimates

Proceedings of a Conference Held July 28-August 3, 1985

By: James Stephen Marron

This volume collects together papers presented at the 1985 Conference in Function Estimation held at Humboldt State University. The papers focus especially on various types of spline estimations and convolution problems. The use of estimation and approximation methods as applied to geophysics, numerical analysis, and nonparametric statistics was a special feature of this conference.

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190

Publisher

American Mathematical Soc.

Published Date

ISBN 10

0821850628

ISBN 13

9780821850626

Higher Homotopy Structures in Topology and Mathematical Physics

Proceedings of an International Conference June 13-15, 1996 at Vassar College, Poughkeepsie, New York, to Honor the Sixtieth Birthday of Jim Stasheff

By: James D. Stasheff,John McCleary

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Higher Homotopy Structures in Topology and Mathematical Physics

Proceedings of an International Conference June 13-15, 1996 at Vassar College, Poughkeepsie, New York, to Honor the Sixtieth Birthday of Jim Stasheff

By: James D. Stasheff,John McCleary

Since the work of Stasheff and Sugawara in the 1960s on recognition of loop space structures on $H$-spaces, the notion of higher homotopies has grown to be a fundamental organizing principle in homotopy theory, differential graded homological algebra and even mathematical physics. This book presents the proceedings from a conference held on the occasion of Stasheff's 60th birthday at Vassar in June 1996. It offers a collection of very high quality papers and includes some fundamental essays on topics that open new areas.

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338

Publisher

American Mathematical Soc.

Published Date

ISBN 10

082180913X

ISBN 13

9780821809136

Complex Geometry and Lie Theory

By: James A. Carlson,Charles Herbert Clemens,David R. Morrison

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Complex Geometry and Lie Theory

By: James A. Carlson,Charles Herbert Clemens,David R. Morrison

In the late 1960s and early 1970s, Phillip Griffiths and his collaborators undertook a study of period mappings and variation of Hodge structure. The motivating problems, which centered on the understanding of algebraic varieties and the algebraic cycles on them, came from algebraic geometry. However, the techiques used were transcendental in nature, drawing heavily on both Lie theory and hermitian differential geometry. Promising approaches were formulated to fundamental questions in the theory of algebraic curves, moduli theory, and the deep interaction between Hodge theory and algebraic cyles. Rapid progress on many fronts was made in the 1970s and 1980s, including the discovery of important connections to other fields, including Nevanlinna theory, integrable systems, rational homotopy theory, harmonic mappings, intersection cohomology, and superstring theory. This volume contains thirteen papers presented during the Symposium on Complex Geometry and Lie Theory held in Sundance, Utah in May 1989. The symposium was designed to review twenty years of interaction between these two fields, concentrating on their links with Hodge theory. The organizers felt that the time was right to examine once again the large issues of understanding the moduli and cycle theory of higher-dimensional varieties, which was the starting point of these developments. The breadth of this collection of papers indicates the continuing growth and vitality of this area of research. Several survey papers are included, which should make the book a valuable resource for graduate students and other researchers who wish to learn about the field. With contributions from some of the field's top researchers, this volume testifies to the breadth and vitality of this area of research.

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358

Publisher

American Mathematical Soc.

Published Date

ISBN 10

0821814923

ISBN 13

9780821814925

Operads in Algebra, Topology and Physics

By: Martin Markl,Steven Shnider,James D. Stasheff

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Operads in Algebra, Topology and Physics

By: Martin Markl,Steven Shnider,James D. Stasheff

Operads are mathematical devices which describe algebraic structures of many varieties and in various categories. From their beginnings in the 1960s, they have developed to encompass such areas as combinatorics, knot theory, moduli spaces, string field theory and deformation quantization.

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362

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American Mathematical Soc.

Published Date

ISBN 10

0821843621

ISBN 13

9780821843628

Structure of the Standard Modules for the Affine Lie Algebra $A^{(1)}_1$

By: James Lepowsky,Mirko Primc

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Structure of the Standard Modules for the Affine Lie Algebra $A^{(1)}_1$

By: James Lepowsky,Mirko Primc

The affine Kac-Moody algebra $A_1 DEGREES{(1)}$ has served as a source of ideas in the representation theory of infinite-dimensional affine Lie algebras. This book develops the calculus of vertex operators to solve the problem of constructing all the standard $A_1 DEGREES{(1)}$-modules in the homogeneou

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American Mathematical Soc.

Published Date

ISBN 10

0821850482

ISBN 13

9780821850480

On Axiomatic Approaches to Vertex Operator Algebras and Modules

By: Igor Frenkel,Yi-Zhi Huang,James Lepowsky

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On Axiomatic Approaches to Vertex Operator Algebras and Modules

By: Igor Frenkel,Yi-Zhi Huang,James Lepowsky

The basic definitions and properties of vertex operator algebras, modules, intertwining operators and related concepts are presented, following a fundamental analogy with Lie algebra theory. The first steps in the development of the general theory are taken, and various natural and useful reformulations of the axioms are given. In particular, tensor products of algebras and modules, adjoint vertex operators and contragradient modules, adjoint intertwining operators and fusion rules are studied in greater depth. This paper lays the monodromy-free axiomatic foundation of the general theory of vertex operator algebras, modules and intertwining operators.

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American Mathematical Soc.

Published Date

ISBN 10

0821825550

ISBN 13

9780821825556

Basic Mathematical Skills with Geometry

By: James A. Streeter

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Basic Mathematical Skills with Geometry

By: James A. Streeter

This interactive CD-ROM is a self-paced tutorial specifically linked to the text and reinforces topics through unlimited opportunities to review concepts and practice problem solving. The CD-ROM contains chapter-and section-specific tutorials, multiple-choice questions with feedback, and algorithmically generated questions. It required virtually no computer training on the part of students and supports IBM and Macintosh computers. In addition, a number of other technology and Web-based ancillaries are under development; they will support the ever-changing technology needs in developmental mathematics.

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830

Published Date

ISBN 10

0072316926

ISBN 13

9780072316926

Beginning Algebra

By: James A. Streeter

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Beginning Algebra

By: James A. Streeter

This interactive CD-ROM is a self-paced tutorial specifically linked to the text and reinforces topics through unlimited opportunities to review concepts and practice problem solving. The CD-ROM contains chapter-and section-specific tutorials, multiiple choice questions with feedback, as well as algorithmically generated questions. It requires virtually no computer training on the part of students and supports IBM and Macintosh computers. In addition, a number of other technology and Web-based ancillaries are under development; they will suppot the ever-changing technology needs in developmental mathematics.

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