{"product_id":"9783031263057","title":"Universitext","description":"\u003ch1\u003eUniversitext\u003c\/h1\u003e \u003ch2\u003eKashaev, Rinat\u003c\/h2\u003e \u003cp\u003e\u003c\/p\u003e\u003cp\u003eThis 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.\u003c\/p\u003e\n\n\u003cp\u003eStarting 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.\u003c\/p\u003e\n\n\u003cp\u003e 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.\u003c\/p\u003e \u003ch3\u003eDetails\u003c\/h3\u003e \u003cp\u003ePublished by: Springer\u003c\/p\u003e \u003cp\u003ePublication Date: 2023-04-15\u003c\/p\u003e \u003cp\u003eFormat: Paperback\u003c\/p\u003e \u003cp\u003eISBN-13: 9783031263057\u003c\/p\u003e \u003cp\u003eDOI: 10.1007\/978-3-031-26306-4\u003c\/p\u003e \u003cp\u003eDimensions: 235cm x155cm\u003c\/p\u003e \u003cp\u003ePages: 165\u003c\/p\u003e ","brand":"Springer International Publishing","offers":[{"title":"Default Title","offer_id":44676792811660,"sku":"9783031263057","price":53.99,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0710\/9545\/1788\/files\/9783031263057.jpg?v=1775729350","url":"https:\/\/fh90cf-fv.myshopify.com\/products\/9783031263057","provider":"Late Knight Books and Services, LLC","version":"1.0","type":"link"}