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Record Nr. |
UNINA9910134869303321 |
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Autore |
Kharchenko Vladislav |
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Titolo |
Quantum Lie Theory : A Multilinear Approach / / by Vladislav Kharchenko |
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Pubbl/distr/stampa |
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Cham : , : Springer International Publishing : , : Imprint : Springer, , 2015 |
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ISBN |
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Edizione |
[1st ed. 2015.] |
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Descrizione fisica |
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1 online resource (XIII, 302 p.) |
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Collana |
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Lecture Notes in Mathematics, , 0075-8434 ; ; 2150 |
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Disciplina |
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Soggetti |
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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 |
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Lingua di pubblicazione |
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Formato |
Materiale a stampa |
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Livello bibliografico |
Monografia |
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Note generali |
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Bibliographic Level Mode of Issuance: Monograph |
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Nota di bibliografia |
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Includes bibliographical references and index. |
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Nota di contenuto |
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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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Sommario/riassunto |
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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 |
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