Coxeter bialgebras:
The goal of this monograph is to develop Hopf theory in the setting of a real reflection arrangement. The central notion is that of a Coxeter bialgebra which generalizes the classical notion of a connected graded Hopf algebra. The authors also introduce the more structured notion of a Coxeter bimono...
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| Hauptverfasser: | , |
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| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Cambridge
Cambridge University Press
2023
|
| Schriftenreihe: | Encyclopedia of mathematics and its applications
186 |
| Schlagworte: | |
| Online-Zugang: | BSB01 BTU01 FHN01 Volltext |
| Zusammenfassung: | The goal of this monograph is to develop Hopf theory in the setting of a real reflection arrangement. The central notion is that of a Coxeter bialgebra which generalizes the classical notion of a connected graded Hopf algebra. The authors also introduce the more structured notion of a Coxeter bimonoid and connect the two notions via a family of functors called Fock functors. These generalize similar functors connecting Hopf monoids in the category of Joyal species and connected graded Hopf algebras. This monograph opens a new chapter in Coxeter theory as well as in Hopf theory, connecting the two. It also relates fruitfully to many other areas of mathematics such as discrete geometry, semigroup theory, associative algebras, algebraic Lie theory, operads, and category theory. It is carefully written, with effective use of tables, diagrams, pictures, and summaries. It will be of interest to students and researchers alike |
| Beschreibung: | Title from publisher's bibliographic system (viewed on 28 Oct 2022) |
| Beschreibung: | 1 Online-Ressource (xix, 875 Seiten) |
| ISBN: | 9781009243759 |
| DOI: | 10.1017/9781009243759 |
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| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
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| dewey-search | 512/.55 |
| dewey-sort | 3512 255 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| discipline_str_mv | Mathematik |
| doi_str_mv | 10.1017/9781009243759 |
| format | Electronic eBook |
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| id | DE-604.BV048580874 |
| illustrated | Not Illustrated |
| index_date | 2024-07-03T21:04:55Z |
| indexdate | 2024-07-10T09:42:05Z |
| institution | BVB |
| isbn | 9781009243759 |
| language | English |
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| physical | 1 Online-Ressource (xix, 875 Seiten) |
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| publishDate | 2023 |
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| publisher | Cambridge University Press |
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| series2 | Encyclopedia of mathematics and its applications 186 |
| spelling | Aguiar, Marcelo 1968- (DE-588)143265873 aut Coxeter bialgebras Marcelo Aguiar, Swapneel Mahajan Cambridge Cambridge University Press 2023 1 Online-Ressource (xix, 875 Seiten) txt rdacontent c rdamedia cr rdacarrier Encyclopedia of mathematics and its applications 186 Title from publisher's bibliographic system (viewed on 28 Oct 2022) The goal of this monograph is to develop Hopf theory in the setting of a real reflection arrangement. The central notion is that of a Coxeter bialgebra which generalizes the classical notion of a connected graded Hopf algebra. The authors also introduce the more structured notion of a Coxeter bimonoid and connect the two notions via a family of functors called Fock functors. These generalize similar functors connecting Hopf monoids in the category of Joyal species and connected graded Hopf algebras. This monograph opens a new chapter in Coxeter theory as well as in Hopf theory, connecting the two. It also relates fruitfully to many other areas of mathematics such as discrete geometry, semigroup theory, associative algebras, algebraic Lie theory, operads, and category theory. It is carefully written, with effective use of tables, diagrams, pictures, and summaries. It will be of interest to students and researchers alike Coxeter groups Hopf algebras Mahajan, Swapneel 1974- (DE-588)143265970 aut Erscheint auch als Druck-Ausgabe 978-1-00-924377-3 https://doi.org/10.1017/9781009243759 Verlag URL des Erstveröffentlichers Volltext |
| spellingShingle | Aguiar, Marcelo 1968- Mahajan, Swapneel 1974- Coxeter bialgebras Coxeter groups Hopf algebras |
| title | Coxeter bialgebras |
| title_auth | Coxeter bialgebras |
| title_exact_search | Coxeter bialgebras |
| title_exact_search_txtP | Coxeter bialgebras |
| title_full | Coxeter bialgebras Marcelo Aguiar, Swapneel Mahajan |
| title_fullStr | Coxeter bialgebras Marcelo Aguiar, Swapneel Mahajan |
| title_full_unstemmed | Coxeter bialgebras Marcelo Aguiar, Swapneel Mahajan |
| title_short | Coxeter bialgebras |
| title_sort | coxeter bialgebras |
| topic | Coxeter groups Hopf algebras |
| topic_facet | Coxeter groups Hopf algebras |
| url | https://doi.org/10.1017/9781009243759 |
| work_keys_str_mv | AT aguiarmarcelo coxeterbialgebras AT mahajanswapneel coxeterbialgebras |