Hopf Algebras:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Singapore
World Scientific
2011
|
| Schriftenreihe: | K & E series on knots and everything
|
| Schlagworte: | |
| Online-Zugang: | FAW01 FAW02 Volltext |
| Beschreibung: | 10.3 Integrals and semisimplicity Preface; Contents; 16. Finite-dimensional Hopf algebras in characteristic 0; 16.1 Characterizations of semisimple Hopf algebras; 16.2 Isomorphism types of Hopf algebras of the same dimension; 16.3 Some very basic classification results; Bibliography; Index; 1. Preliminaries; 1.1 Notation and terminology conventions; 1.2 Rank of a tensor; 1.3 Topological aspects of vector space duals; Chapter notes; 2. Coalgebras; 2.1 Algebras and coalgebras, basic definitions; 2.2 Comatrix identities, the fundamental theorem of coalgebras; 2.3 The dual algebra; 2.4 The wedge product; 2.5 The dual coalgebra 2.6 Double duals2.7 The cofree coalgebra on a vector space; Chapter notes; 3. Representations of coalgebras; 3.1 Rational modules of the dual algebra; 3.2 Comodules; 3.3 Mr and Mr; 3.4 The coradical of a coalgebra; 3.5 Injective comodules; 3.6 Coalgebras which are submodules of their dual algebras; 3.7 Indecomposable coalgebras; Chapter notes; 4. The coradical .ltration and related structures; 4.1 Filtrations of coalgebras; 4.2 The wedge product and the coradical filtration; 4.3 Idempotents and the coradical filtration; 4.4 Graded algebras and coalgebras 4.5 The cofree pointed irreducible coalgebra on a vector space4.6 The radical of the dual algebra; 4.7 Free pointed coalgebras associated to coalgebras; 4.8 Linked simple subcoalgebras; Chapter notes; 5. Bialgebras; 5.1 Basic definitions and results; 5.2 The dual bialgebra; 5.3 The free bialgebra on a coalgebra and related constructions; 5.4 The universal enveloping algebra; 5.5 The cofree bialgebra on an algebra; 5.6 Filtrations and gradings of bialgebras; 5.7 Representations of bialgebras; Chapter notes; 6. The convolution algebra; 6.1 Definition and basic properties 6.2 Invertible elements in the convolution algebraChapter notes; 7. Hopf algebras; 7.1 Definition of Hopf algebra, the antipode; 7.2 Q-binomial symbols; 7.3 Two families of examples; 7.4 The dual Hopf algebra; 7.5 The free Hopf algebra on a coalgebra; 7.6 When a bialgebra is a Hopf algebra; 7.7 Two-cocycles, pairings, and skew pairings of bialgebras; 7.8 Twists of bialgebras; 7.9 Filtrations and gradings on Hopf algebras; 7.10 The cofree pointed irreducible Hopf algebra on an algebra; 7.11 The shuffle algebra; Chapter notes; 8. Hopf modules and co-Hopf modules 8.1 Definition of Hopf module and examples8.2 The structure of Hopf modules; 8.3 Co-Hopf modules; 8.4 A basic co-Hopf module and its dual; Chapter notes; 9. Hopf algebras as modules over Hopf subalgebras; 9.1 Filtrations whose base term is a Hopf subalgebra; 9.2 Relative Hopf modules; 9.3 When Hopf algebras free over their Hopf subalgebras; 9.4 An example of a Hopf algebra which is not free over some Hopf subalgebra; Chapter notes; 10. Integrals; 10.1 Definition of integrals for a bialgebra and its dual algebra; 10.2 Existence and uniqueness of integrals for a Hopf algebra The book provides a detailed account of basic coalgebra and Hopf algebra theory with emphasis on Hopf algebras which are pointed, semisimple, quasitriangular, or are of certain other quantum groups. It is intended to be a graduate text as well as a research monograph |
| Beschreibung: | 1 Online-Ressource (584 pages) |
| ISBN: | 1280669403 9781280669408 9789814338660 9814338664 |
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| 500 | |a 10.3 Integrals and semisimplicity | ||
| 500 | |a Preface; Contents; 16. Finite-dimensional Hopf algebras in characteristic 0; 16.1 Characterizations of semisimple Hopf algebras; 16.2 Isomorphism types of Hopf algebras of the same dimension; 16.3 Some very basic classification results; Bibliography; Index; 1. Preliminaries; 1.1 Notation and terminology conventions; 1.2 Rank of a tensor; 1.3 Topological aspects of vector space duals; Chapter notes; 2. Coalgebras; 2.1 Algebras and coalgebras, basic definitions; 2.2 Comatrix identities, the fundamental theorem of coalgebras; 2.3 The dual algebra; 2.4 The wedge product; 2.5 The dual coalgebra | ||
| 500 | |a 2.6 Double duals2.7 The cofree coalgebra on a vector space; Chapter notes; 3. Representations of coalgebras; 3.1 Rational modules of the dual algebra; 3.2 Comodules; 3.3 Mr and Mr; 3.4 The coradical of a coalgebra; 3.5 Injective comodules; 3.6 Coalgebras which are submodules of their dual algebras; 3.7 Indecomposable coalgebras; Chapter notes; 4. The coradical .ltration and related structures; 4.1 Filtrations of coalgebras; 4.2 The wedge product and the coradical filtration; 4.3 Idempotents and the coradical filtration; 4.4 Graded algebras and coalgebras | ||
| 500 | |a 4.5 The cofree pointed irreducible coalgebra on a vector space4.6 The radical of the dual algebra; 4.7 Free pointed coalgebras associated to coalgebras; 4.8 Linked simple subcoalgebras; Chapter notes; 5. Bialgebras; 5.1 Basic definitions and results; 5.2 The dual bialgebra; 5.3 The free bialgebra on a coalgebra and related constructions; 5.4 The universal enveloping algebra; 5.5 The cofree bialgebra on an algebra; 5.6 Filtrations and gradings of bialgebras; 5.7 Representations of bialgebras; Chapter notes; 6. The convolution algebra; 6.1 Definition and basic properties | ||
| 500 | |a 6.2 Invertible elements in the convolution algebraChapter notes; 7. Hopf algebras; 7.1 Definition of Hopf algebra, the antipode; 7.2 Q-binomial symbols; 7.3 Two families of examples; 7.4 The dual Hopf algebra; 7.5 The free Hopf algebra on a coalgebra; 7.6 When a bialgebra is a Hopf algebra; 7.7 Two-cocycles, pairings, and skew pairings of bialgebras; 7.8 Twists of bialgebras; 7.9 Filtrations and gradings on Hopf algebras; 7.10 The cofree pointed irreducible Hopf algebra on an algebra; 7.11 The shuffle algebra; Chapter notes; 8. Hopf modules and co-Hopf modules | ||
| 500 | |a 8.1 Definition of Hopf module and examples8.2 The structure of Hopf modules; 8.3 Co-Hopf modules; 8.4 A basic co-Hopf module and its dual; Chapter notes; 9. Hopf algebras as modules over Hopf subalgebras; 9.1 Filtrations whose base term is a Hopf subalgebra; 9.2 Relative Hopf modules; 9.3 When Hopf algebras free over their Hopf subalgebras; 9.4 An example of a Hopf algebra which is not free over some Hopf subalgebra; Chapter notes; 10. Integrals; 10.1 Definition of integrals for a bialgebra and its dual algebra; 10.2 Existence and uniqueness of integrals for a Hopf algebra | ||
| 500 | |a The book provides a detailed account of basic coalgebra and Hopf algebra theory with emphasis on Hopf algebras which are pointed, semisimple, quasitriangular, or are of certain other quantum groups. It is intended to be a graduate text as well as a research monograph | ||
| 650 | 4 | |a Mathematics | |
| 650 | 7 | |a MATHEMATICS / Algebra / Linear |2 bisacsh | |
| 650 | 4 | |a Mathematik | |
| 650 | 4 | |a Hopf algebras | |
| 650 | 0 | 7 | |a Hopf-Algebra |0 (DE-588)4160646-2 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Hopf-Algebra |0 (DE-588)4160646-2 |D s |
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Datensatz im Suchindex
| _version_ | 1804175473986502656 |
|---|---|
| any_adam_object | |
| author | Radford, David E. |
| author_facet | Radford, David E. |
| author_role | aut |
| author_sort | Radford, David E. |
| author_variant | d e r de der |
| building | Verbundindex |
| bvnumber | BV043081484 |
| collection | ZDB-4-EBA |
| ctrlnum | (OCoLC)794328359 (DE-599)BVBBV043081484 |
| dewey-full | 512/.55 512.55 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
| dewey-raw | 512/.55 512.55 |
| dewey-search | 512/.55 512.55 |
| dewey-sort | 3512 255 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Electronic eBook |
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| id | DE-604.BV043081484 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T07:16:51Z |
| institution | BVB |
| isbn | 1280669403 9781280669408 9789814338660 9814338664 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-028505676 |
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| owner_facet | DE-1046 DE-1047 |
| physical | 1 Online-Ressource (584 pages) |
| psigel | ZDB-4-EBA ZDB-4-EBA FAW_PDA_EBA |
| publishDate | 2011 |
| publishDateSearch | 2011 |
| publishDateSort | 2011 |
| publisher | World Scientific |
| record_format | marc |
| series2 | K & E series on knots and everything |
| spelling | Radford, David E. Verfasser aut Hopf Algebras Singapore World Scientific 2011 1 Online-Ressource (584 pages) txt rdacontent c rdamedia cr rdacarrier K & E series on knots and everything 10.3 Integrals and semisimplicity Preface; Contents; 16. Finite-dimensional Hopf algebras in characteristic 0; 16.1 Characterizations of semisimple Hopf algebras; 16.2 Isomorphism types of Hopf algebras of the same dimension; 16.3 Some very basic classification results; Bibliography; Index; 1. Preliminaries; 1.1 Notation and terminology conventions; 1.2 Rank of a tensor; 1.3 Topological aspects of vector space duals; Chapter notes; 2. Coalgebras; 2.1 Algebras and coalgebras, basic definitions; 2.2 Comatrix identities, the fundamental theorem of coalgebras; 2.3 The dual algebra; 2.4 The wedge product; 2.5 The dual coalgebra 2.6 Double duals2.7 The cofree coalgebra on a vector space; Chapter notes; 3. Representations of coalgebras; 3.1 Rational modules of the dual algebra; 3.2 Comodules; 3.3 Mr and Mr; 3.4 The coradical of a coalgebra; 3.5 Injective comodules; 3.6 Coalgebras which are submodules of their dual algebras; 3.7 Indecomposable coalgebras; Chapter notes; 4. The coradical .ltration and related structures; 4.1 Filtrations of coalgebras; 4.2 The wedge product and the coradical filtration; 4.3 Idempotents and the coradical filtration; 4.4 Graded algebras and coalgebras 4.5 The cofree pointed irreducible coalgebra on a vector space4.6 The radical of the dual algebra; 4.7 Free pointed coalgebras associated to coalgebras; 4.8 Linked simple subcoalgebras; Chapter notes; 5. Bialgebras; 5.1 Basic definitions and results; 5.2 The dual bialgebra; 5.3 The free bialgebra on a coalgebra and related constructions; 5.4 The universal enveloping algebra; 5.5 The cofree bialgebra on an algebra; 5.6 Filtrations and gradings of bialgebras; 5.7 Representations of bialgebras; Chapter notes; 6. The convolution algebra; 6.1 Definition and basic properties 6.2 Invertible elements in the convolution algebraChapter notes; 7. Hopf algebras; 7.1 Definition of Hopf algebra, the antipode; 7.2 Q-binomial symbols; 7.3 Two families of examples; 7.4 The dual Hopf algebra; 7.5 The free Hopf algebra on a coalgebra; 7.6 When a bialgebra is a Hopf algebra; 7.7 Two-cocycles, pairings, and skew pairings of bialgebras; 7.8 Twists of bialgebras; 7.9 Filtrations and gradings on Hopf algebras; 7.10 The cofree pointed irreducible Hopf algebra on an algebra; 7.11 The shuffle algebra; Chapter notes; 8. Hopf modules and co-Hopf modules 8.1 Definition of Hopf module and examples8.2 The structure of Hopf modules; 8.3 Co-Hopf modules; 8.4 A basic co-Hopf module and its dual; Chapter notes; 9. Hopf algebras as modules over Hopf subalgebras; 9.1 Filtrations whose base term is a Hopf subalgebra; 9.2 Relative Hopf modules; 9.3 When Hopf algebras free over their Hopf subalgebras; 9.4 An example of a Hopf algebra which is not free over some Hopf subalgebra; Chapter notes; 10. Integrals; 10.1 Definition of integrals for a bialgebra and its dual algebra; 10.2 Existence and uniqueness of integrals for a Hopf algebra The book provides a detailed account of basic coalgebra and Hopf algebra theory with emphasis on Hopf algebras which are pointed, semisimple, quasitriangular, or are of certain other quantum groups. It is intended to be a graduate text as well as a research monograph Mathematics MATHEMATICS / Algebra / Linear bisacsh Mathematik Hopf algebras Hopf-Algebra (DE-588)4160646-2 gnd rswk-swf Hopf-Algebra (DE-588)4160646-2 s 1\p DE-604 http://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&db=nlabk&AN=457156 Aggregator Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Radford, David E. Hopf Algebras Mathematics MATHEMATICS / Algebra / Linear bisacsh Mathematik Hopf algebras Hopf-Algebra (DE-588)4160646-2 gnd |
| subject_GND | (DE-588)4160646-2 |
| title | Hopf Algebras |
| title_auth | Hopf Algebras |
| title_exact_search | Hopf Algebras |
| title_full | Hopf Algebras |
| title_fullStr | Hopf Algebras |
| title_full_unstemmed | Hopf Algebras |
| title_short | Hopf Algebras |
| title_sort | hopf algebras |
| topic | Mathematics MATHEMATICS / Algebra / Linear bisacsh Mathematik Hopf algebras Hopf-Algebra (DE-588)4160646-2 gnd |
| topic_facet | Mathematics MATHEMATICS / Algebra / Linear Mathematik Hopf algebras Hopf-Algebra |
| url | http://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&db=nlabk&AN=457156 |
| work_keys_str_mv | AT radforddavide hopfalgebras |