Quantum Lie theory : a multilinear approach / Vladislav Kharchenko.
By: Kharchenko, Vladislav.
Material type: TextSeries: 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: 512.482Item type  Current location  Call number  Status  Date due  Barcode  Item holds  

Books 
ISI Library, Kolkata

512.482 K45 (Browse shelf)  Available  136748 
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512.482 Ia11 Lie algebras and applications  512.482 In61 Generalized lie theory in mathematics physics and beyond  512.482 K45 Geometry of infinitedimensional groups  512.482 K45 Quantum Lie theory :  512.482 R869 Symmetric spaces and the KashiwaraVergne method /  512.482 T171 Hilbert's fifth problem and related topics /  512.482 T171 Expansion in finite simple groups of Lie type / 
Includes bibliographical references and index.
1. Elements of Noncommutative Algebra 
2. PoincareBirkhoffWitt Basis 
3. Quantizations of KacMoody Algebras 
4. Algebra of SkewPrimitive 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 1520 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 PBWtype theorem; quantum deformations of KacMoody algebras; generic and symmetric quantum Lie operations; the Nichols algebras; the GurevichManin Lie algebras; and ShestakovUmirbaev 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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