A course on Hopf algebras / Rinat Kashaev.
2023
QA613.8 .K37 2023
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Details
Title
A course on Hopf algebras / Rinat Kashaev.
Author
Kashaev, Rinat, author.
ISBN
9783031263064 electronic book
3031263065 electronic book
9783031263057
3031263057
3031263065 electronic book
9783031263057
3031263057
Published
Cham, Switzerland : Springer, 2023.
Language
English
Description
1 online resource (xv, 165 pages).
Item Number
10.1007/978-3-031-26306-4 doi
Call Number
QA613.8 .K37 2023
Dewey Decimal Classification
512/.55
Summary
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.
Bibliography, etc. Note
Includes bibliographical references and index.
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Access limited to authorized users.
Source of Description
Online resource; title from PDF title page (SpringerLink, viewed April 18, 2023).
Series
Universitext, 2191-6675
Available in Other Form
Print version: 9783031263057
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