| 期刊全稱 | A Course on Hopf Algebras | | 影響因子2023 | Rinat Kashaev | | 視頻video | http://file.papertrans.cn/141/140518/140518.mp4 | | 發(fā)行地址 | Includes advanced applications to knot theory, such as the construction of solutions to Yang–Baxter equations.Uses string diagrams to facilitate understanding.Assumes only minimal background for most | | 學(xué)科分類 | Universitext | | 圖書封面 |  | | 影響因子 | 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, m | | Pindex | Textbook 2023 |
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