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A Course on Hopf Algebras / by Rinat Kashaev.
Springer Nature - Springer Mathematics and Statistics eBooks 2023 English International Available online
View online- Format:
- Book
- Author/Creator:
- Kashaev, Rinat, author.
- Series:
- Universitext, 2191-6675
- Language:
- English
- Subjects (All):
- Associative rings.
- Associative algebras.
- Manifolds (Mathematics).
- Algebras, Linear.
- Topological groups.
- Lie groups.
- Mathematical physics.
- Algebra, Homological.
- Associative Rings and Algebras.
- Manifolds and Cell Complexes.
- Linear Algebra.
- Topological Groups and Lie Groups.
- Mathematical Physics.
- Category Theory, Homological Algebra.
- Local Subjects:
- Associative Rings and Algebras.
- Manifolds and Cell Complexes.
- Linear Algebra.
- Topological Groups and Lie Groups.
- Mathematical Physics.
- Category Theory, Homological Algebra.
- Physical Description:
- 1 online resource (173 pages)
- Edition:
- 1st ed. 2023.
- Place of Publication:
- Cham : Springer International Publishing : Imprint: Springer, 2023.
- 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.
- Notes:
- Includes bibliographical references and index.
- Other Format:
- Print version: Kashaev, Rinat A Course on Hopf Algebras
- ISBN:
- 9783031263064
- OCLC:
- 1376375062
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