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010   $a9783031263064$b(electronic bk.)
010   $z9783031263057
024 7 $a10.1007/978-3-031-26306-4
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035   $a(Au-PeEL)EBL7236551
035   $a(DE-He213)978-3-031-26306-4
035   $a(OCoLC)1376375062
035   $a(PPN)269655719
035   $a(CKB)26435292300041
035   $a(EXLCZ)9926435292300041
100   $a20230413d2023      u|         0
101 0 $aeng
135   $aurcnu||||||||
181   $ctxt$2rdacontent
182   $cc$2rdamedia
183   $acr$2rdacarrier
200 12$aA Course on Hopf Algebras /$fby Rinat Kashaev
205   $a1st ed. 2023.
210  1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2023.
215   $a1 online resource (173 pages)
225 1 $aUniversitext,$x2191-6675
311 08$aPrint version: Kashaev, Rinat A Course on Hopf Algebras Cham : Springer International Publishing AG,c2023 9783031263057 
320   $aIncludes bibliographical references and index.
330   $aThis textbook provides a concise, visual introduction to Hopf algebras and their application to knot theory, most notably the construction of solutions of the Yang?Baxter equations. Starting with a reformulation of the definition of a group in terms of structural maps as motivation for the definition of a Hopf algebra, the book introduces the related algebraic notions: algebras, coalgebras, bialgebras, convolution algebras, modules, comodules. Next, Drinfel?d?s quantum double construction is achieved through the important notion of the restricted (or finite) dual of a Hopf algebra, which allows one to work purely algebraically, without completions. As a result, in applications to knot theory, to any Hopf algebra with invertible antipode one can associate a universal invariant of long knots. These constructions are elucidated in detailed analyses of a few examples of Hopf algebras. The presentation of the material is mostly based on multilinear algebra, with all definitions carefully formulated and proofs self-contained. The general theory is illustrated with concrete examples, and many technicalities are handled with the help of visual aids, namely string diagrams. As a result, most of this text is accessible with minimal prerequisites and can serve as the basis of introductory courses to beginning graduate students.
410  0$aUniversitext,$x2191-6675
606   $aAssociative rings
606   $aAssociative algebras
606   $aManifolds (Mathematics)
606   $aAlgebras, Linear
606   $aTopological groups
606   $aLie groups
606   $aMathematical physics
606   $aAlgebra, Homological
606   $aAssociative Rings and Algebras
606   $aManifolds and Cell Complexes
606   $aLinear Algebra
606   $aTopological Groups and Lie Groups
606   $aMathematical Physics
606   $aCategory Theory, Homological Algebra
615  0$aAssociative rings.
615  0$aAssociative algebras.
615  0$aManifolds (Mathematics)
615  0$aAlgebras, Linear.
615  0$aTopological groups.
615  0$aLie groups.
615  0$aMathematical physics.
615  0$aAlgebra, Homological.
615 14$aAssociative Rings and Algebras.
615 24$aManifolds and Cell Complexes.
615 24$aLinear Algebra.
615 24$aTopological Groups and Lie Groups.
615 24$aMathematical Physics.
615 24$aCategory Theory, Homological Algebra.
676   $a512.55
700   $aKashaev$b Rinat$01352756
801  0$bMiAaPQ
801  1$bMiAaPQ
801  2$bMiAaPQ
912   $a9910698648803321
996   $aA Course on Hopf Algebras$93200517
997   $aUNINA