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Quantum Lie Theory : A Multilinear Approach / by Vladislav Kharchenko
(Lecture Notes in Mathematics. ISSN:16179692 ; 2150)
版 | 1st ed. 2015. |
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出版者 | Cham : Springer International Publishing : Imprint: Springer |
出版年 | 2015 |
大きさ | XIII, 302 p : online resource |
著者標目 | *Kharchenko, Vladislav author SpringerLink (Online service) |
件 名 | LCSH:Associative rings LCSH:Associative algebras LCSH:Nonassociative rings LCSH:Group theory LCSH:Quantum physics FREE:Associative Rings and Algebras FREE:Non-associative Rings and Algebras FREE:Group Theory and Generalizations FREE:Quantum Physics |
一般注記 | 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 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 HTTP:URL=https://doi.org/10.1007/978-3-319-22704-7 |
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電子ブック | 配架場所 | 資料種別 | 巻 次 | 請求記号 | 状 態 | 予約 | コメント | ISBN | 刷 年 | 利用注記 | 指定図書 | 登録番号 |
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電子ブック | オンライン | 電子ブック |
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Springer eBooks | 9783319227047 |
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EB00210968 |
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