Ivan Penkov's Books

Classical Lie Algebras at Infinity

By: Ivan Penkov,Crystal Hoyt

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Classical Lie Algebras at Infinity

By: Ivan Penkov,Crystal Hoyt

Originating from graduate topics courses given by the first author, this book functions as a unique text-monograph hybrid that bridges a traditional graduate course to research level representation theory. The exposition includes an introduction to the subject, some highlights of the theory and recent results in the field, and is therefore appropriate for advanced graduate students entering the field as well as research mathematicians wishing to expand their knowledge. The mathematical background required varies from chapter to chapter, but a standard course on Lie algebras and their representations, along with some knowledge of homological algebra, is necessary. Basic algebraic geometry and sheaf cohomology are needed for Chapter 10. Exercises of various levels of difficulty are interlaced throughout the text to add depth to topical comprehension. The unifying theme of this book is the structure and representation theory of infinite-dimensional locally reductive Lie algebras and superalgebras. Chapters 1-6 are foundational; each of the last 4 chapters presents a self-contained study of a specialized topic within the larger field. Lie superalgebras and flag supermanifolds are discussed in Chapters 3, 7, and 10, and may be skipped by the reader.

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Page Count

245

Publisher

Springer Nature

Published Date

ISBN 10

3030896609

ISBN 13

9783030896607

Glasses and the Glass Transition

By: Ivan S. Gutzow,Oleg V. Mazurin,J¿rn W. P. Schmelzer,Snejana V. Todorova,Boris B. Petroff,Alexander I. Priven

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Glasses and the Glass Transition

By: Ivan S. Gutzow,Oleg V. Mazurin,J¿rn W. P. Schmelzer,Snejana V. Todorova,Boris B. Petroff,Alexander I. Priven

Written by renowned researchers in the field, this up-to-date treatise fills the gap for a high-level work discussing current materials and processes. It covers all the steps involved, from vitrification, relaxation and viscosity, right up to the prediction of glass properties, paving the way for improved methods and applications. For solid state physicists and chemists, materials scientists, and those working in the ceramics industry. With a preface by L. David Pye and a foreword by Edgar D. Zanotto

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Page Count

360

Publisher

John Wiley & Sons

Published Date

ISBN 10

3527636544

ISBN 13

9783527636549

The Vitreous State

Thermodynamics, Structure, Rheology, and Crystallization

By: Ivan S. Gutzow,Jürn W.P. Schmelzer

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The Vitreous State

Thermodynamics, Structure, Rheology, and Crystallization

By: Ivan S. Gutzow,Jürn W.P. Schmelzer

This book summarizes the experimental evidence and modern classical and theoretical approaches in understanding the vitreous state, from structural problems, over equilibrium and non-equilibrium thermodynamics, to statistical physics. Glasses, and especially silicate glasses, are only the best known representatives of this particular physical state of matter. Other typical representatives include organic polymer glasses, and many other easily vitrifying organic and inorganic substances, technically important materials, amidst them vitreous water and vitrified aqueous solutions, and also many metallic alloy systems. Some of these systems only form glasses under particular conditions, e.g. through ultra-rapid cooling. This book describes the properties and the formation of both every-day technical glasses and especially of such more exotic forms of vitreous matter. It is a unique source of knowledge and new ideas for materials scientists, engineers and researchers working on condensed matter. The new edition emphasizes latest experimental findings and modern theories, explaining the kinetics of glass formation, the relaxation and stabilization of glasses and their crystallization in terms of new models, derived from the framework of the thermodynamics of irreversible processes. It shows how the properties of common technical glasses, window glass, or the vitreous ice kernel of comets can be used to develop a new understanding of the existence of matter in various, unusual forms. The described theories can even find application for the description of lasers and interesting unusual processes in the universe.

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Page Count

566

Publisher

Springer Science & Business Media

Published Date

ISBN 10

3642346332

ISBN 13

9783642346330

Classical Lie Algebras at Infinity

By: Ivan Penkov,Crystal Hoyt

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Classical Lie Algebras at Infinity

By: Ivan Penkov,Crystal Hoyt

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245

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Springer Nature

Published Date

ISBN 10

3030896609

ISBN 13

9783030896607

Modular Interfaces: Modular Lie Algebras, Quantum Groups, and Lie Superalgebras

Modular Lie Algebras, Quantum Groups, and Lie Superalgebras

By: Vyjayanthi Chari

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Modular Interfaces: Modular Lie Algebras, Quantum Groups, and Lie Superalgebras

Modular Lie Algebras, Quantum Groups, and Lie Superalgebras

By: Vyjayanthi Chari

This book is a collection of papers dedicated to Richard E. Block, whose research has been largely devoted to the study of Lie algebras of prime characteristic (specifically the classification of simple Lie algebras). The volume presents proceedings of a conference held at the University of California at Riverside in February 1994 on the occasion of his retirement. The conference focused on the interplay between the theory of Lie algebras of prime characteristic, quantum groups, and Lie superalgebras. Titles in this series are co-published with International Press, Cambridge, MA, USA.

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Page Count

172

Publisher

American Mathematical Soc.

Published Date

ISBN 10

082180748X

ISBN 13

9780821807484

Highlights in Lie Algebraic Methods

By: Anthony Joseph,Anna Melnikov,Ivan Penkov

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Highlights in Lie Algebraic Methods

By: Anthony Joseph,Anna Melnikov,Ivan Penkov

This volume consists of expository and research articles that highlight the various Lie algebraic methods used in mathematical research today. Key topics discussed include spherical varieties, Littelmann Paths and Kac–Moody Lie algebras, modular representations, primitive ideals, representation theory of Artin algebras and quivers, Kac–Moody superalgebras, categories of Harish–Chandra modules, cohomological methods, and cluster algebras.

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Page Count

227

Publisher

Birkhäuser

Published Date

ISBN 10

0817682732

ISBN 13

9780817682736

Glass

Selected Properties and Crystallization

By: Jürn W. P. Schmelzer

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Glass

Selected Properties and Crystallization

By: Jürn W. P. Schmelzer

“This book contains overviews on technologically important classes of glasses, their treatment to achieve desired properties, theoretical approaches for the description of structure-property relationships, and new concepts in the theoretical treatment of crystallization in glass-forming systems. It contains overviews about the state of the art and about specific features for the analysis and application of important classes of glass-forming systems, and describes new developments in theoretical interpretation by well-known glass scientists. Thus, the book offers comprehensive and abundant information that is difficult to come by or has not yet been made public.” Edgar Dutra Zanotto (Center for Research, Technology and Education in Vitreous Materials, Brazil) Glass, written by a team of renowned researchers and experienced book authors in the field, presents general features of glasses and glass transitions. Different classes of glassforming systems, such as silicate glasses, metallic glasses, and polymers, are exemplified. In addition, the wide field of phase formation processes and their effect on glasses and their properties is studied both from a theoretical and experimental point of view.

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Page Count

578

Publisher

Walter de Gruyter GmbH & Co KG

Published Date

ISBN 10

3110368102

ISBN 13

9783110368109

Book's by Ivan Penkov

Classical Lie Algebras at Infinity

Classical Lie Algebras at Infinity

Glasses and the Glass Transition

Glasses and the Glass Transition

The Vitreous State

The Vitreous State

Classical Lie Algebras at Infinity

Classical Lie Algebras at Infinity

Modular Interfaces: Modular Lie Algebras, Quantum Groups, and Lie Superalgebras

Modular Interfaces: Modular Lie Algebras, Quantum Groups, and Lie Superalgebras

Highlights in Lie Algebraic Methods

Highlights in Lie Algebraic Methods

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