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Quantum Lie Theory : A Multilinear Approach / by Vladislav Kharchenko
(Lecture Notes in Mathematics. ISSN:16179692 ; 2150)
Edition | 1st ed. 2015. |
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Publisher | Cham : Springer International Publishing : Imprint: Springer |
Year | 2015 |
Size | XIII, 302 p : online resource |
Authors | *Kharchenko, Vladislav author SpringerLink (Online service) |
Subjects | 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 |
Notes | 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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E-Book | Location | Media type | Volume | Call No. | Status | Reserve | Comments | ISBN | Printed | Restriction | Designated Book | Barcode No. |
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E-Book | 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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