Kashaev R A Course on Hopf Algebras 2023
Date: 14 April 2023 | Posted by: BeMyLove
Kashaev R A Course on Hopf Algebras 2023 | 5.84 MB
English | 173 Pages
Title: A Course on Hopf Algebras
Author: Rinat Kashaev
Year: 2023
Description:
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, most of this text is accessible with minimal prerequisites and can serve as the basis of introductory courses to beginning graduate students.
DOWNLOAD:
https://rapidgator.net/file/79d92c1ae3ef4678d544e6620dabb598/Kashaev_R._A_Course_on_Hopf_Algebras_2023.rar
https://uploadgig.com/file/download/76192b9584f5333a/Kashaev_R._A_Course_on_Hopf_Algebras_2023.rar
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, most of this text is accessible with minimal prerequisites and can serve as the basis of introductory courses to beginning graduate students.
DOWNLOAD:
https://rapidgator.net/file/79d92c1ae3ef4678d544e6620dabb598/Kashaev_R._A_Course_on_Hopf_Algebras_2023.rar
https://uploadgig.com/file/download/76192b9584f5333a/Kashaev_R._A_Course_on_Hopf_Algebras_2023.rar
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