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Quantum Lie Theory : A Multilinear Approach / by Vladislav Kharchenko.
Math/Physics/Astronomy Library QA3 .L28 v.1-999 470,523,830,849:2nd ed. v.1000-1722,1762,1781,1799-2099,2100-2192-2218 2219-2223-2258,2260-2271,2273-2274-2277,2279-2281,2283-2289,2291,2293-2294,2296,2298-2299,2300-2311,2313-2366,2368-2379,2381-2382 2385,2388-2389
Mixed Availability
LIBRA QA3 .L28 Scattered vols.
Mixed Availability
- Format:
- Book
- Author/Creator:
- Kharchenko, Vladislav., Author.
- Series:
- Lecture Notes in Mathematics, 0075-8434 ; 2150
- Language:
- English
- Subjects (All):
- Associative rings.
- Rings (Algebra).
- Nonassociative rings.
- Group theory.
- Quantum theory.
- Associative Rings and Algebras.
- Non-associative Rings and Algebras.
- Group Theory and Generalizations.
- Quantum Physics.
- Local Subjects:
- Associative Rings and Algebras.
- Non-associative Rings and Algebras.
- Group Theory and Generalizations.
- Quantum Physics.
- Physical Description:
- 1 online resource (XIII, 302 p.)
- Edition:
- 1st ed. 2015.
- Place of Publication:
- Cham : Springer International Publishing : Imprint: Springer, 2015.
- Language Note:
- English
- 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.
- Contents:
- Elements of noncommutative algebra
- Poincar´e-Birkhoff-Witt basis
- Quantizations of Kac-Moody algebras
- Algebra of skew-primitive elements
- Multilinear operations
- Braided Hopf algebras
- Binary structures
- Algebra of primitive nonassociative polynomials.
- Notes:
- Bibliographic Level Mode of Issuance: Monograph
- Includes bibliographical references and index.
- ISBN:
- 3-319-22704-1
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