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100   $a20151224d2015      u|         0
101 0 $aeng
135   $aurnn|008mamaa
181   $ctxt
182   $cc
183   $acr
200 10$aQuantum Lie Theory $eA Multilinear Approach /$fby Vladislav Kharchenko
205   $a1st ed. 2015.
210  1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2015.
215   $a1 online resource (XIII, 302 p.) 
225 1 $aLecture Notes in Mathematics,$x0075-8434 ;$v2150
300   $aBibliographic Level Mode of Issuance: Monograph
311   $a3-319-22703-3 
320   $aIncludes bibliographical references and index.
327   $aElements of noncommutative algebra -- PoincarŽe-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.
330   $aThis is an introduction to the mathematics behind the phrase ?quantum Lie algebra?. The numerous attempts over the last 15-20 years to define a quantum Lie algebra as an elegant algebraic object with a binary ?quantum? Lie bracket have not been widely accepted. In this book, an alternative approach is developed that includes multivariable operations. Among the problems discussed are the following: a PBW-type theorem; quantum deformations of Kac--Moody algebras; generic and symmetric quantum Lie operations; the Nichols algebras; the Gurevich--Manin  Lie algebras;  and Shestakov--Umirbaev  operations for the Lie theory of nonassociative products.  Opening with an introduction for beginners and continuing as a textbook for graduate students in physics and mathematics, the book can also be used as a reference by more advanced readers. With the exception of the introductory chapter, the content of this monograph has not previously appeared in book form.
410  0$aLecture Notes in Mathematics,$x0075-8434 ;$v2150
606   $aAssociative rings
606   $aRings (Algebra)
606   $aNonassociative rings
606   $aGroup theory
606   $aQuantum theory
606   $aAssociative Rings and Algebras$3https://scigraph.springernature.com/ontologies/product-market-codes/M11027
606   $aNon-associative Rings and Algebras$3https://scigraph.springernature.com/ontologies/product-market-codes/M11116
606   $aGroup Theory and Generalizations$3https://scigraph.springernature.com/ontologies/product-market-codes/M11078
606   $aQuantum Physics$3https://scigraph.springernature.com/ontologies/product-market-codes/P19080
615  0$aAssociative rings.
615  0$aRings (Algebra)
615  0$aNonassociative rings.
615  0$aGroup theory.
615  0$aQuantum theory.
615 14$aAssociative Rings and Algebras.
615 24$aNon-associative Rings and Algebras.
615 24$aGroup Theory and Generalizations.
615 24$aQuantum Physics.
676   $a512.55
700   $aKharchenko$b Vladislav$4aut$4http://id.loc.gov/vocabulary/relators/aut$0716357
801  0$bMiAaPQ
801  1$bMiAaPQ
801  2$bMiAaPQ
906   $aBOOK
912   $a9910134869303321
996   $aQuantum lie theory$91387927
997   $aUNINA