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Quantum Lie theory : a multilinear approach / Vladislav Kharchenko.

By: Kharchenko, Vladislav.
Material type: TextTextSeries: Lecture notes in mathematics ; 2150.Publisher: Switzerland : Springer, 2015Description: xiii, 302 p. : 24 cm.ISBN: 9783319227030 (alk. paper).Subject(s): Lie algebras | Quantum theoryDDC classification: 512.482
Contents:
1. Elements of Noncommutative Algebra -- 2. Poincare-Birkhoff-Witt Basis -- 3. Quantizations of Kac-Moody Algebras -- 4. Algebra of Skew-Primitive Elements -- 5. Multilinear Operations -- 6. Braided Hopf Algebras -- 7. Binary Structures -- 8. Algebra of Primitive Nonassociative Polynomials -- References -- Index.
Summary: This is an introduction to the mathematics behind the phrase “quantum Lie algebra”. The numerous attempts over the last 15-20 years to define a quantum Lie algebra as an elegant algebraic object with a binary “quantum” Lie bracket have not been widely accepted. In this book, an alternative approach is developed that includes multivariable operations. Among the problems discussed are the following: a PBW-type theorem; quantum deformations of Kac--Moody algebras; generic and symmetric quantum Lie operations; the Nichols algebras; the Gurevich--Manin Lie algebras; and Shestakov--Umirbaev operations for the Lie theory of nonassociative products. Opening with an introduction for beginners and continuing as a textbook for graduate students in physics and mathematics, the book can also be used as a reference by more advanced readers. With the exception of the introductory chapter, the content of this monograph has not previously appeared in book form.
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Item type Current location Call number Status Date due Barcode Item holds
Books Books ISI Library, Kolkata
 
512.482 K45 (Browse shelf) Available 136748
Total holds: 0

Includes bibliographical references and index.

1. Elements of Noncommutative Algebra --
2. Poincare-Birkhoff-Witt Basis --
3. Quantizations of Kac-Moody Algebras --
4. Algebra of Skew-Primitive Elements --
5. Multilinear Operations --
6. Braided Hopf Algebras --
7. Binary Structures --
8. Algebra of Primitive Nonassociative Polynomials --
References --
Index.

This is an introduction to the mathematics behind the phrase “quantum Lie algebra”. The numerous attempts over the last 15-20 years to define a quantum Lie algebra as an elegant algebraic object with a binary “quantum” Lie bracket have not been widely accepted. In this book, an alternative approach is developed that includes multivariable operations. Among the problems discussed are the following: a PBW-type theorem; quantum deformations of Kac--Moody algebras; generic and symmetric quantum Lie operations; the Nichols algebras; the Gurevich--Manin Lie algebras; and Shestakov--Umirbaev operations for the Lie theory of nonassociative products. Opening with an introduction for beginners and continuing as a textbook for graduate students in physics and mathematics, the book can also be used as a reference by more advanced readers. With the exception of the introductory chapter, the content of this monograph has not previously appeared in book form.

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