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A course on Hopf algebras

Kashaev, Rinat.

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A course on Hopf algebras

Record Type:	Electronic resources : Monograph/item
Title/Author:	A course on Hopf algebras/ by Rinat Kashaev.
Author:	Kashaev, Rinat.
Published:	Cham :Springer International Publishing : : 2023.,
Description:	xv, 165 p. :ill., digital ;24 cm.
Contained By:	Springer Nature eBook
Subject:	Hopf algebras. -
Online resource:	https://doi.org/10.1007/978-3-031-26306-4
ISBN:	9783031263064

A course on Hopf algebras
Kashaev, Rinat.

A course on Hopf algebras[electronic resource] /by Rinat Kashaev. - Cham :Springer International Publishing :2023. - xv, 165 p. :ill., digital ;24 cm. - Universitext,2191-6675. - Universitext..

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.

ISBN: 9783031263064

Standard No.: 10.1007/978-3-031-26306-4doiSubjects--Topical Terms:

706147
Hopf algebras.

LC Class. No.: QA613.8

Dewey Class. No.: 512.55

A course on Hopf algebras
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100 1 $a Kashaev, Rinat. $3 3632360
245 1 2 $a A course on Hopf algebras $h [electronic resource] / $c by Rinat Kashaev.
260 $a Cham : $b Springer International Publishing : $b Imprint: Springer, $c 2023.
300 $a xv, 165 p. : $b ill., digital ; $c 24 cm.
490 1 $a Universitext, $x 2191-6675
520 $a 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.
650 0 $a Hopf algebras. $3 706147
650 1 4 $a Associative Rings and Algebras. $3 897405
650 2 4 $a Manifolds and Cell Complexes. $3 3538507
650 2 4 $a Linear Algebra. $3 3338825
650 2 4 $a Topological Groups and Lie Groups. $3 3593340
650 2 4 $a Mathematical Physics. $3 1542352
650 2 4 $a Category Theory, Homological Algebra. $3 899944
710 2 $a SpringerLink (Online service) $3 836513
773 0 $t Springer Nature eBook
830 0 $a Universitext. $3 812115
856 4 0 $u https://doi.org/10.1007/978-3-031-26306-4
950 $a Mathematics and Statistics (SpringerNature-11649)