Alexander Molev's Books

Yangians and Classical Lie Algebras

By: Alexander Molev

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Yangians and Classical Lie Algebras

By: Alexander Molev

The Yangians and twisted Yangians are remarkable associative algebras taking their origins from the work of St. Petersburg's school of mathematical physics in the 1980s. This book is an introduction to the theory of Yangians and twisted Yangians, with a particular emphasis on the relationship with the classical matrix Lie algebras.

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Page Count

422

Publisher

American Mathematical Soc.

Published Date

ISBN 10

0821843745

ISBN 13

9780821843741

Sugawara Operators for Classical Lie Algebras

By: Alexander Molev:

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Sugawara Operators for Classical Lie Algebras

By: Alexander Molev:

The celebrated Schur-Weyl duality gives rise to effective ways of constructing invariant polynomials on the classical Lie algebras. The emergence of the theory of quantum groups in the 1980s brought up special matrix techniques which allowed one to extend these constructions beyond polynomial invariants and produce new families of Casimir elements for finite-dimensional Lie algebras. Sugawara operators are analogs of Casimir elements for the affine Kac-Moody algebras. The goal of this book is to describe algebraic structures associated with the affine Lie algebras, including affine vertex algebras, Yangians, and classical -algebras, which have numerous ties with many areas of mathematics and mathematical physics, including modular forms, conformal field theory, and soliton equations. An affine version of the matrix technique is developed and used to explain the elegant constructions of Sugawara operators, which appeared in the last decade. An affine analogue of the Harish-Chandra isomorphism connects the Sugawara operators with the classical -algebras, which play the role of the Weyl group invariants in the finite-dimensional theory.

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Page Count

321

Publisher

American Mathematical Soc.

Published Date

ISBN 10

1470436590

ISBN 13

9781470436599

Infinite Dimensional Lie Superalgebras

By: Yuri Bahturin,Alexander V. Mikhalev,Viktor M. Petrogradsky,Mikhail V. Zaicev

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Infinite Dimensional Lie Superalgebras

By: Yuri Bahturin,Alexander V. Mikhalev,Viktor M. Petrogradsky,Mikhail V. Zaicev

The aim of the series is to present new and important developments in pure and applied mathematics. Well established in the community over two decades, it offers a large library of mathematics including several important classics. The volumes supply thorough and detailed expositions of the methods and ideas essential to the topics in question. In addition, they convey their relationships to other parts of mathematics. The series is addressed to advanced readers wishing to thoroughly study the topic. Editorial Board Lev Birbrair, Universidade Federal do Ceará, Fortaleza, Brasil Victor P. Maslov, Russian Academy of Sciences, Moscow, Russia Walter D. Neumann, Columbia University, New York, USA Markus J. Pflaum, University of Colorado, Boulder, USA Dierk Schleicher, Jacobs University, Bremen, Germany

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Page Count

261

Publisher

Walter de Gruyter

Published Date

ISBN 10

3110851202

ISBN 13

9783110851205

Combinatorial Aspects of Lie Superalgebras

By: Alexander A. Mikhalev,Andrej A. Zolotykh

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Combinatorial Aspects of Lie Superalgebras

By: Alexander A. Mikhalev,Andrej A. Zolotykh

Combinatorial Aspects of Lie Superalgebras emphasizes the algorithmic and computational aspects of the combinatorial techniques of Lie superalgebras. It is written primarily for mathematicians and scientists who do not have a background in the field of infinite dimensional Lie superalgebras, but who realize the potential uses of the results. Consequently, the discussions provided on the applications of Lie superalgebras theory are clear and comprehensive and, throughout the text, primary attention is given to algorithms and examples. The examples illustrate theoretical results, and the algorithms, which can be used for symbolic calculations with Lie superalgebras, are based on basic and generally applicable rules and theorems. Combinatorial Aspects of Lie Superalgebras contains comprehensive literature citations and provides an excellent reference on the techniques and results of combinatorial theory of Lie superalgebras. Programs that have been developed by the authors for computation are included on a diskette at the back of the book, and complete directions for use are provided.

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Page Count

276

Publisher

CRC Press

Published Date

ISBN 10

0849389607

ISBN 13

9780849389603

Sugawara Operators for Classical Lie Algebras

By: Alexander Molev:

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Sugawara Operators for Classical Lie Algebras

By: Alexander Molev:

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Solve jigsaw puzzle

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Page Count

321

Publisher

American Mathematical Soc.

Published Date

ISBN 10

1470436590

ISBN 13

9781470436599

Yangians and Classical Lie Algebras

By: Alexander Molev

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Yangians and Classical Lie Algebras

By: Alexander Molev

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Solve jigsaw puzzle

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Page Count

422

Publisher

American Mathematical Soc.

Published Date

ISBN 10

0821843745

ISBN 13

9780821843741

Book's by Alexander Molev

Yangians and Classical Lie Algebras

Yangians and Classical Lie Algebras

Sugawara Operators for Classical Lie Algebras

Sugawara Operators for Classical Lie Algebras

Infinite Dimensional Lie Superalgebras

Infinite Dimensional Lie Superalgebras

Combinatorial Aspects of Lie Superalgebras

Combinatorial Aspects of Lie Superalgebras

Sugawara Operators for Classical Lie Algebras

Sugawara Operators for Classical Lie Algebras

Yangians and Classical Lie Algebras

Yangians and Classical Lie Algebras

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