{"product_id":"a-course-on-hopf-algebras-9783031263057","title":"A Course on Hopf Algebras","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\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.\u003cp\u003e\u003c\/p\u003e  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.\u003cp\u003e\u003c\/p\u003e  \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\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e- 1. Groups and Hopf Algebras. - 2. Constructions of Algebras, Coalgebras, Bialgebras, and Hopf Algebras. - 3. The Restricted Dual of an Algebra. - 4. The Restricted Dual of Hopf Algebras: Examples of Calculations. - 5. The Quantum Double. - 6. Applications in Knot Theory. ","brand":"Springer International Publishing AG","offers":[{"title":"Default Title","offer_id":51360331333975,"sku":"9783031263057","price":40.49,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9783031263057.jpg?v=1754127359","url":"https:\/\/bookcurl.com\/products\/a-course-on-hopf-algebras-9783031263057","provider":"Book Curl","version":"1.0","type":"link"}