{"product_id":"a-course-on-hopf-algebras-von-rinat-kashaev","title":"A Course on Hopf Algebras","description":"\n                                \n                \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                \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                \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\n                            \n            \u003cdiv class=\"aw-variant-hidden-subtitle-div\" id=\"aw-variant-subtitle-9783031263057\"\u003e\u003ch3\u003e\u003c\/h3\u003e\u003c\/div\u003e","brand":"Autorenwelt Shop","offers":[{"title":"Softcover - 9783031263057","offer_id":46499434234181,"sku":"9783031263057","price":53.49,"currency_code":"EUR","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0940\/0622\/files\/b5d0f0bd-7d82-463a-befb-2eff5896dc8a.jpg?v=1772170143","url":"https:\/\/shop.autorenwelt.de\/products\/a-course-on-hopf-algebras-von-rinat-kashaev","provider":"Autorenwelt Shop","version":"1.0","type":"link"}