A Course on Hopf Algebras
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 definitio...
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| Natura: | Elettronico eBook |
| Lingua: | inglese |
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Cham :
Springer International Publishing : Imprint: Springer,
2023.
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| Edizione: | 1st ed. 2023. |
| Serie: | Universitext,
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| Accesso online: | https://doi.org/10.1007/978-3-031-26306-4 |
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| 100 | 1 | |a Kashaev, Rinat. |e author. |0 (orcid)0000-0001-5705-5561 |1 https://orcid.org/0000-0001-5705-5561 |4 aut |4 http://id.loc.gov/vocabulary/relators/aut | |
| 245 | 1 | 2 | |a A Course on Hopf Algebras |h [electronic resource] / |c by Rinat Kashaev. |
| 250 | |a 1st ed. 2023. | ||
| 264 | 1 | |a Cham : |b Springer International Publishing : |b Imprint: Springer, |c 2023. | |
| 300 | |a 1 online resource (XV, 165 p.). | ||
| 336 | |a text |b txt |2 rdacontent | ||
| 337 | |a computer |b c |2 rdamedia | ||
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| 341 | 0 | |b Table of contents navigation |2 onix | |
| 341 | 0 | |b Single logical reading order |2 onix | |
| 341 | 0 | |b Short alternative textual descriptions |2 onix | |
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| 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. | ||
| 532 | 8 | |a Accessibility summary: This PDF does Not fully comply with PDF/UA standards but does include limited screen reader support, descriptions for Non-text content (such as images and graphs), bookmarks for easy navigation, and searchable, selectable text. Users of assistive technologies may experience difficulty navigating or interpreting content in this document. We recognise the importance of accessibility and welcome queries about accessibility for any of our products. If you have a question or an access need, please get in touch with us via https://www.springernature.com/gp/info/accessibility | |
| 532 | 8 | |a Inaccessible, or known limited accessibility | |
| 532 | 8 | |a No reading system accessibility options actively disabled | |
| 532 | 8 | |a Publisher contact for further accessibility information: accessibilitysupport@springernature.com | |
| 588 | |a Print version record. | ||
| 650 | 0 | |a Associative rings. | |
| 650 | 0 | |a Associative algebras. | |
| 650 | 0 | |a Manifolds (Mathematics). | |
| 650 | 0 | |a Algebras, Linear. | |
| 650 | 0 | |a Topological groups. | |
| 650 | 0 | |a Lie groups. | |
| 650 | 0 | |a Mathematical physics. | |
| 650 | 0 | |a Algebra, Homological. | |
| 650 | 1 | 4 | |a Associative Rings and Algebras. |
| 650 | 2 | 4 | |a Manifolds and Cell Complexes. |
| 650 | 2 | 4 | |a Linear Algebra. |
| 650 | 2 | 4 | |a Topological Groups and Lie Groups. |
| 650 | 2 | 4 | |a Mathematical Physics. |
| 650 | 2 | 4 | |a Category Theory, Homological Algebra. |
| 710 | 2 | |a SpringerLink (Online service) | |
| 773 | 0 | |t Springer Nature eBook | |
| 776 | 0 | 8 | |i Printed edition: |z 9783031263057 |
| 776 | 0 | 8 | |i Printed edition: |z 9783031263071 |
| 830 | 0 | |a Universitext, |x 2191-6675 | |
| 856 | 4 | 0 | |u https://doi.org/10.1007/978-3-031-26306-4 |
| 912 | |a ZDB-2-SMA | ||
| 912 | |a ZDB-2-SXMS | ||
| 950 | |a Mathematics and Statistics (SpringerNature-11649) | ||
| 950 | |a Mathematics and Statistics (R0) (SpringerNature-43713) | ||