Name: A Course on Hopf Algebras (en Inglés)
Price: 189.72 PEN
Availability: InStock
Author: Kashaev, Rinat
ISBN: 9783031263057

portada A Course on Hopf Algebras (en Inglés)

Formato

Libro Físico

Autor

Rinat Kashaev

Editorial

Springer

Idioma

Inglés

N° páginas

165

Encuadernación

Tapa Blanda

Dimensiones

23.2 x 15.0 x 1.2 cm

Peso

0.27 kg.

ISBN13

9783031263057

N° edición

Categorías

Álgebra
Topología

A Course on Hopf Algebras (en Inglés)

Rinat Kashaev (Autor) · Springer · Tapa Blanda

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Reseña del libro "A Course on Hopf Algebras (en Inglés)"

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.