Alexander Kirillov Jr.'s Books

An Introduction to Lie Groups and Lie Algebras

By: Alexander A. Kirillov

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An Introduction to Lie Groups and Lie Algebras

By: Alexander A. Kirillov

This book is an introduction to semisimple Lie algebras. It is concise and informal, with numerous exercises and examples.

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Page Count

237

Publisher

Cambridge University Press

Published Date

ISBN 10

0521889693

ISBN 13

9780521889698

Quiver Representations and Quiver Varieties

By: Alexander Kirillov Jr.

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Quiver Representations and Quiver Varieties

By: Alexander Kirillov Jr.

This book is an introduction to the theory of quiver representations and quiver varieties, starting with basic definitions and ending with Nakajima's work on quiver varieties and the geometric realization of Kac–Moody Lie algebras. The first part of the book is devoted to the classical theory of quivers of finite type. Here the exposition is mostly self-contained and all important proofs are presented in detail. The second part contains the more recent topics of quiver theory that are related to quivers of infinite type: Coxeter functor, tame and wild quivers, McKay correspondence, and representations of Euclidean quivers. In the third part, topics related to geometric aspects of quiver theory are discussed, such as quiver varieties, Hilbert schemes, and the geometric realization of Kac–Moody algebras. Here some of the more technical proofs are omitted; instead only the statements and some ideas of the proofs are given, and the reader is referred to original papers for details. The exposition in the book requires only a basic knowledge of algebraic geometry, differential geometry, and the theory of Lie groups and Lie algebras. Some sections use the language of derived categories; however, the use of this language is reduced to a minimum. The many examples make the book accessible to graduate students who want to learn about quivers, their representations, and their relations to algebraic geometry and Lie algebras.

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Page Count

311

Publisher

American Mathematical Soc.

Published Date

ISBN 10

1470423073

ISBN 13

9781470423070

Differential Topology, Infinite-Dimensional Lie Algebras, and Applications

D.B. Fuchs' 60th anniversary collection

By: Alexander Astashkevich,Serge Tabachnikov

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Differential Topology, Infinite-Dimensional Lie Algebras, and Applications

D.B. Fuchs' 60th anniversary collection

By: Alexander Astashkevich,Serge Tabachnikov

This volume presents contributions by leading experts in the field. The articles are dedicated to D.B. Fuchs on the occasion of his 60th birthday. Contributors to the book were directly influenced by Professor Fuchs, and include his students, friends, and professional colleagues. In addition to their research, they offer personal reminicences about Professor Fuchs, giving insight into the history of Russian mathematics.

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Page Count

362

Publisher

American Mathematical Soc.

Published Date

ISBN 10

082182032X

ISBN 13

9780821820322

An Introduction to Lie Groups and Lie Algebras

By: Alexander A. Kirillov

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An Introduction to Lie Groups and Lie Algebras

By: Alexander A. Kirillov

This book is an introduction to semisimple Lie algebras. It is concise and informal, with numerous exercises and examples.

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Page Count

237

Publisher

Cambridge University Press

Published Date

ISBN 10

0521889693

ISBN 13

9780521889698

Lectures on Tensor Categories and Modular Functors

By: Bojko Bakalov,Alexander A. Kirillov

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Lectures on Tensor Categories and Modular Functors

By: Bojko Bakalov,Alexander A. Kirillov

This book gives an exposition of the relations among the following three topics: monoidal tensor categories (such as a category of representations of a quantum group), 3-dimensional topological quantum field theory, and 2-dimensional modular functors (which naturally arise in 2-dimensional conformal field theory). The following examples are discussed in detail: the category of representations of a quantum group at a root of unity and the Wess-Zumino-Witten modular functor. The idea that these topics are related first appeared in the physics literature in the study of quantum field theory. Pioneering works of Witten and Moore-Seiberg triggered an avalanche of papers, both physical and mathematical, exploring various aspects of these relations. Upon preparing to lecture on the topic at MIT, however, the authors discovered that the existing literature was difficult and that there were gaps to fill. The text is wholly expository and finely succinct. It gathers results, fills existing gaps, and simplifies some proofs. The book makes an important addition to the existing literature on the topic. It would be suitable as a course text at the advanced-graduate level.

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Page Count

232

Publisher

American Mathematical Soc.

Published Date

ISBN 10

0821826867

ISBN 13

9780821826867

Lectures on Representation Theory and Knizhnik-Zamolodchikov Equations

By: Pavel I. Etingof,Igor Frenkel,Alexander A. Kirillov

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Lectures on Representation Theory and Knizhnik-Zamolodchikov Equations

By: Pavel I. Etingof,Igor Frenkel,Alexander A. Kirillov

This text is devoted to mathematical structures arising in conformal field theory and the q-deformations. The authors give a self-contained exposition of the theory of Knizhnik-Zamolodchikov equations and related topics. No previous knowledge of physics is required. The text is suitable for a one-semester graduate course and is intended for graduate students and research mathematicians interested in mathematical physics.

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Page Count

215

Publisher

American Mathematical Soc.

Published Date

ISBN 10

0821804960

ISBN 13

9780821804964

Harmonic Analysis for Engineers and Applied Scientists

Updated and Expanded Edition

By: Gregory S. Chirikjian,Alexander B. Kyatkin

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Harmonic Analysis for Engineers and Applied Scientists

Updated and Expanded Edition

By: Gregory S. Chirikjian,Alexander B. Kyatkin

Although the Fourier transform is among engineering's most widely used mathematical tools, few engineers realize that the extension of harmonic analysis to functions on groups holds great potential for solving problems in robotics, image analysis, mechanics, and other areas. This self-contained approach, geared toward readers with a standard background in engineering mathematics, explores the widest possible range of applications to fields such as robotics, mechanics, tomography, sensor calibration, estimation and control, liquid crystal analysis, and conformational statistics of macromolecules. Harmonic analysis is explored in terms of particular Lie groups, and the text deals with only a limited number of proofs, focusing instead on specific applications and fundamental mathematical results. Forming a bridge between pure mathematics and the challenges of modern engineering, this updated and expanded volume offers a concrete, accessible treatment that places the general theory in the context of specific groups.

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Page Count

881

Publisher

Courier Dover Publications

Published Date

ISBN 10

0486795640

ISBN 13

9780486795645

Quadratic Algebras

By: Alexander Polishchuk,Leonid Positselski

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Quadratic Algebras

By: Alexander Polishchuk,Leonid Positselski

This book introduces recent developments in the study of algebras defined by quadratic relations. One of the main problems in the study of these (and similarly defined) algebras is how to control their size. A central notion in solving this problem is the notion of a Koszul algebra, which was introduced in 1970 by S. Priddy and then appeared in many areas of mathematics, such as algebraic geometry, representation theory, non commutative geometry, $K$-theory, number theory, and non commutative linear algebra.The authors give a coherent exposition of the theory of quadratic and Koszul algebras, including various definitions of Koszulness, duality theory, Poincare-Birkhoff-Witt-type theorems for Koszul algebras, and the Koszul deformation principle. In the concluding chapter of the book, they explain a surprising connection between Koszul algebras and one-dependent discrete-time stochastic processes. The book can be used by graduate students and researchers working in algebra and any of the above-mentioned areas of mathematics.

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Page Count

176

Publisher

American Mathematical Soc.

Published Date

ISBN 10

0821838342

ISBN 13

9780821838341

Schumann Resonance for Tyros

Essentials of Global Electromagnetic Resonance in the Earth–Ionosphere Cavity

By: Alexander Nickolaenko,Masashi Hayakawa

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Schumann Resonance for Tyros

Essentials of Global Electromagnetic Resonance in the Earth–Ionosphere Cavity

By: Alexander Nickolaenko,Masashi Hayakawa

Schumann resonance has been studied for more than half a century. The field became popular among researchers of the terrestrial environment using natural sources of electromagnetic radiation—lightning strokes, primarily—and now many Schumann observatories have been established around the world. A huge number of publications can be found in the literature, the most recent collection of which was presented in a special Schumann resonance section of the journal Radio Science in 2007. The massive publications, however, impede finding information about how to organize measurements and start observations of global electromagnetic resonance. Relevant information is scattered throughout many publications, which are not always available. The goal of this book is to collect all necessary data in a single edition in order to describe the demands of the necessary equipment and the field-site as well as the impact of industrial and natural interference, and to demonstrate typical results and obstacles often met in measurements. The authors not only provide representative results but also describe unusual radio signals in the extremely low-frequency (ELF) band and discuss signals in the adjacent frequency ranges.

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Page Count

355

Publisher

Springer Science & Business Media

Published Date

ISBN 10

4431543589

ISBN 13

9784431543589

Sea-Ice and Iceberg Sedimentation in the Ocean

Recent and Past

By: Alexander P. Lisitzin

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Sea-Ice and Iceberg Sedimentation in the Ocean

Recent and Past

By: Alexander P. Lisitzin

This reference book for researchers working on glacial sediments provides a complete overview of the various glacial deposits in the ocean. It presents a collection of worldwide data on glacio-marine phenomena.

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Page Count

584

Publisher

Springer Science & Business Media

Published Date

ISBN 10

3540679650

ISBN 13

9783540679653

Plasma Physics and Engineering

By: Alexander Fridman

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Plasma Physics and Engineering

By: Alexander Fridman

Plasma engineering is a rapidly expanding area of science and technology with increasing numbers of engineers using plasma processes over a wide range of applications. A current partial list would include: electronics, energetics, fuel conversion, ozone generation, treatment of polymers and othermaterials, synthesis of new materials, production of

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Page Count

882

Publisher

CRC Press

Published Date

ISBN 10

1482293633

ISBN 13

9781482293630

Probabilistic and Statistical Aspects of Quantum Theory

By: Alexander S. Holevo

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Probabilistic and Statistical Aspects of Quantum Theory

By: Alexander S. Holevo

This book is devoted to aspects of the foundations of quantum mechanics in which probabilistic and statistical concepts play an essential role. The main part of the book concerns the quantitative statistical theory of quantum measurement, based on the notion of positive operator-valued measures. During the past years there has been substantial progress in this direction, stimulated to a great extent by new applications such as Quantum Optics, Quantum Communication and high-precision experiments. The questions of statistical interpretation, quantum symmetries, theory of canonical commutation relations and Gaussian states, uncertainty relations as well as new fundamental bounds concerning the accuracy of quantum measurements, are discussed in this book in an accessible yet rigorous way. Compared to the first edition, there is a new Supplement devoted to the hidden variable issue. Comments and the bibliography have also been extended and updated.

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Page Count

336

Publisher

Springer Science & Business Media

Published Date

ISBN 10

8876423788

ISBN 13

9788876423789

Ribosomes

By: Alexander S. Spirin

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Ribosomes

By: Alexander S. Spirin

Dr. Spirin is a world authority on ribosomes and has published two earlier books in this area in English. This text is for advanced undergraduates and beginning graduate students and will cover the structure, function, and biosynthesis of ribosomes. Ribosomes are important in protein synthesis, which is currently a hot topic in many different areas of research.

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Page Count

417

Publisher

Springer Science & Business Media

Published Date

ISBN 10

0306468158

ISBN 13

9780306468155

Conformal and Potential Analysis in Hele-Shaw Cells

By: Björn Gustafsson,Alexander Vasil'ev

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Conformal and Potential Analysis in Hele-Shaw Cells

By: Björn Gustafsson,Alexander Vasil'ev

This monograph presents recent and new ideas arising from the study of problems of planar fluid dynamics, and which are interesting from the point of view of geometric function theory and potential theory. the book is concerned with geometric problems for Hele-Shaw flows. Additionally, Hele-Shaw flows on parameter spaces are discussed, and connections with string theory are revealed. Assumes a graduate level understanding of real and complex analysis, and fluid mechanics.

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Page Count

235

Publisher

Springer Science & Business Media

Published Date

ISBN 10

3764377046

ISBN 13

9783764377045

Classical and Stochastic Laplacian Growth

By: Björn Gustafsson,Razvan Teodorescu,Alexander Vasil’ev

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Classical and Stochastic Laplacian Growth

By: Björn Gustafsson,Razvan Teodorescu,Alexander Vasil’ev

This monograph covers a multitude of concepts, results, and research topics originating from a classical moving-boundary problem in two dimensions (idealized Hele-Shaw flows, or classical Laplacian growth), which has strong connections to many exciting modern developments in mathematics and theoretical physics. Of particular interest are the relations between Laplacian growth and the infinite-size limit of ensembles of random matrices with complex eigenvalues; integrable hierarchies of differential equations and their spectral curves; classical and stochastic Löwner evolution and critical phenomena in two-dimensional statistical models; weak solutions of hyperbolic partial differential equations of singular-perturbation type; and resolution of singularities for compact Riemann surfaces with anti-holomorphic involution. The book also provides an abundance of exact classical solutions, many explicit examples of dynamics by conformal mapping as well as a solid foundation of potential theory. An extensive bibliography covering over twelve decades of results and an introduction rich in historical and biographical details complement the eight main chapters of this monograph. Given its systematic and consistent notation and background results, this book provides a self-contained resource. It is accessible to a wide readership, from beginner graduate students to researchers from various fields in natural sciences and mathematics.

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Page Count

329

Publisher

Springer

Published Date

ISBN 10

3319082876

ISBN 13

9783319082875

Introduction to Lie Groups and Lie Algebras

By: Alexander A. Kirillov

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Introduction to Lie Groups and Lie Algebras

By: Alexander A. Kirillov

With roots in the nineteenth century, Lie theory has since found many and varied applications in mathematics and mathematical physics, to the point where it is now regarded as a classical branch of mathematics in its own right. This graduate text focuses on the study of semisimple Lie algebras, developing the necessary theory along the way. The material covered ranges from basic definitions of Lie groups to the classification of finite-dimensional representations of semisimple Lie algebras. Written in an informal style, this is a contemporary introduction to the subject which emphasizes the main concepts of the proofs and outlines the necessary technical details, allowing the material to be conveyed concisely. Based on a lecture course given by the author at the State University of New York at Stony Brook, the book includes numerous exercises and worked examples and is ideal for graduate courses on Lie groups and Lie algebras.

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