A Course on Hopf Algebras / / by Rinat Kashaev
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| Autore: |
Kashaev Rinat
|
| Titolo: |
A Course on Hopf Algebras / / by Rinat Kashaev
|
| Pubblicazione: | Cham : , : Springer International Publishing : , : Imprint : Springer, , 2023 |
| Edizione: | 1st ed. 2023. |
| Descrizione fisica: | 1 online resource (173 pages) |
| Disciplina: | 512.55 |
| Soggetto topico: | 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 | |
| Nota di bibliografia: | Includes bibliographical references and index. |
| Sommario/riassunto: | 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. |
| Titolo autorizzato: | A Course on Hopf Algebras |
| ISBN: | 9783031263064 |
| 9783031263057 | |
| Formato: | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione: | Inglese |
| Record Nr.: | 9910698648803321 |
| Lo trovi qui: | Univ. Federico II |
| Opac: | Controlla la disponibilità qui |
Serie:
Universitext, . 2191-6675