02912nam 2200505 450 991069864880332120231204131024.09783031263064(electronic bk.)978303126305710.1007/978-3-031-26306-4(MiAaPQ)EBC7236551(Au-PeEL)EBL7236551(DE-He213)978-3-031-26306-4(OCoLC)1376375062(PPN)269655719(EXLCZ)992643529230004120230611d2023 uy 0engurcnu||||||||txtrdacontentcrdamediacrrdacarrierA course on Hopf algebras /Rinat Kashaev1st ed. 2023.Cham, Switzerland :Springer Nature Switzerland AG,[2023]©20231 online resource (173 pages)Universitext,2191-6675Print version: Kashaev, Rinat A Course on Hopf Algebras Cham : Springer International Publishing AG,c2023 9783031263057 Includes bibliographical references and index.This 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.Universitext,2191-6675Hopf algebrasÀlgebres de HopfthubLlibres electrònicsthubHopf algebras.Àlgebres de Hopf512.55Kashaev Rinat1352756MiAaPQMiAaPQMiAaPQ9910698648803321A Course on Hopf Algebras3200517UNINA