| Descript |
1 online resource (xiii, 302 pages) : illustrations, digital ; 24 cm |
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text txt rdacontent |
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computer c rdamedia |
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online resource cr rdacarrier |
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text file PDF rda |
| Series |
Lecture notes in mathematics, 0075-8434 ; 2150
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Lecture notes in mathematics ; 2150
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| Note |
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 |
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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 |
| Host Item |
Springer eBooks
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| Subject |
Lie algebras
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Quantum theory
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Mathematics
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Associative Rings and Algebras
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Non-associative Rings and Algebras
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Group Theory and Generalizations
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Quantum Physics
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| Alt Author |
SpringerLink (Online service)
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