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020 _a9783319227047
_9978-3-319-22704-7
024 7 _a10.1007/978-3-319-22704-7
_2doi
050 4 _aQA251.5
072 7 _aPBF
_2bicssc
072 7 _aMAT002010
_2bisacsh
072 7 _aPBF
_2thema
082 0 4 _a512.46
_223
100 1 _aKharchenko, Vladislav.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
245 1 0 _aQuantum Lie Theory
_h[electronic resource] :
_bA Multilinear Approach /
_cby Vladislav Kharchenko.
250 _a1st ed. 2015.
264 1 _aCham :
_bSpringer International Publishing :
_bImprint: Springer,
_c2015.
300 _aXIII, 302 p.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aLecture Notes in Mathematics,
_x0075-8434 ;
_v2150
505 0 _aElements 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.
520 _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.
650 0 _aAlgebra.
650 0 _aGroup theory.
650 0 _aQuantum theory.
650 1 4 _aAssociative Rings and Algebras.
_0http://scigraph.springernature.com/things/product-market-codes/M11027
650 2 4 _aNon-associative Rings and Algebras.
_0http://scigraph.springernature.com/things/product-market-codes/M11116
650 2 4 _aGroup Theory and Generalizations.
_0http://scigraph.springernature.com/things/product-market-codes/M11078
650 2 4 _aQuantum Physics.
_0http://scigraph.springernature.com/things/product-market-codes/P19080
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9783319227030
776 0 8 _iPrinted edition:
_z9783319227054
830 0 _aLecture Notes in Mathematics,
_x0075-8434 ;
_v2150
856 4 0 _uhttps://doi.org/10.1007/978-3-319-22704-7
912 _aZDB-2-SMA
912 _aZDB-2-LNM
999 _c11921
_d11921