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A course on Hopf algebras

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	A course on Hopf algebrasby Rinat Kashaev.
作者:	Kashaev, Rinat.
出版者:	Cham :Springer International Publishing :2023.
面頁冊數:	xv, 165 p. :ill., digital ;24 cm.
Contained By:	Springer Nature eBook
標題:	Hopf algebras.
電子資源:	https://doi.org/10.1007/978-3-031-26306-4
ISBN:	9783031263064$q(electronic bk.)

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$q(electronic bk.)

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

190853
Hopf algebras.

LC Class. No.: QA613.8

Dewey Class. No.: 512.55

A course on Hopf algebras
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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.
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650 1 4 $a Associative Rings and Algebras. $3 274818
650 2 4 $a Manifolds and Cell Complexes. $3 913127
650 2 4 $a Linear Algebra. $3 821215
650 2 4 $a Topological Groups and Lie Groups. $3 915048
650 2 4 $a Mathematical Physics. $3 522725
650 2 4 $a Category Theory, Homological Algebra. $3 275954
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