001463275 000__ 03592cam\a22005897i\4500
001463275 001__ 1463275
001463275 003__ OCoLC
001463275 005__ 20230601003313.0
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001463275 019__ $$a1375993037
001463275 020__ $$a9783031263064$$qelectronic book
001463275 020__ $$a3031263065$$qelectronic book
001463275 020__ $$z9783031263057
001463275 020__ $$z3031263057
001463275 0247_ $$a10.1007/978-3-031-26306-4$$2doi
001463275 035__ $$aSP(OCoLC)1376375062
001463275 040__ $$aGW5XE$$beng$$erda$$epn$$cGW5XE$$dYDX$$dEBLCP$$dYDX
001463275 049__ $$aISEA
001463275 050_4 $$aQA613.8$$b.K37 2023
001463275 08204 $$a512/.55$$223/eng/20230418
001463275 1001_ $$aKashaev, Rinat,$$eauthor.$$0(orcid)0000-0001-5705-5561$$1https://orcid.org/0000-0001-5705-5561
001463275 24512 $$aA course on Hopf algebras /$$cRinat Kashaev.
001463275 264_1 $$aCham, Switzerland :$$bSpringer,$$c2023.
001463275 300__ $$a1 online resource (xv, 165 pages).
001463275 336__ $$atext$$btxt$$2rdacontent
001463275 337__ $$acomputer$$bc$$2rdamedia
001463275 338__ $$aonline resource$$bcr$$2rdacarrier
001463275 4901_ $$aUniversitext,$$x2191-6675
001463275 504__ $$aIncludes bibliographical references and index.
001463275 506__ $$aAccess limited to authorized users.
001463275 520__ $$aThis textbook provides a concise, visual introduction to Hopf algebras and their application to knot theory, most notably the construction of solutions of the Yang-Baxter equations. Starting with a reformulation of the definition of a group in terms of structural maps as motivation for the definition of a Hopf algebra, the book introduces the related algebraic notions: algebras, coalgebras, bialgebras, convolution algebras, modules, comodules. Next, Drinfel'd's quantum double construction is achieved through the important notion of the restricted (or finite) dual of a Hopf algebra, which allows one to work purely algebraically, without completions. As a result, in applications to knot theory, to any Hopf algebra with invertible antipode one can associate a universal invariant of long knots. These constructions are elucidated in detailed analyses of a few examples of Hopf algebras. The presentation of the material is mostly based on multilinear algebra, with all definitions carefully formulated and proofs self-contained. The general theory is illustrated with concrete examples, and many technicalities are handled with the help of visual aids, namely string diagrams. As a result, most of this text is accessible with minimal prerequisites and can serve as the basis of introductory courses to beginning graduate students.
001463275 588__ $$aOnline resource; title from PDF title page (SpringerLink, viewed April 18, 2023).
001463275 650_0 $$aHopf algebras.
001463275 655_0 $$aElectronic books.
001463275 77608 $$iPrint version: $$z3031263057$$z9783031263057$$w(OCoLC)1363101906
001463275 830_0 $$aUniversitext,$$x2191-6675
001463275 852__ $$bebk
001463275 85640 $$3Springer Nature$$uhttps://univsouthin.idm.oclc.org/login?url=https://link.springer.com/10.1007/978-3-031-26306-4$$zOnline Access$$91397441.1
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001463275 980__ $$aBIB
001463275 980__ $$aEBOOK
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