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
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| Schriftenreihe: | Encyclopedia of mathematics and its applications
186 |
| Schlagworte: | |
| Online-Zugang: | BSB01 BTU01 FHN01 URL des Erstveröffentlichers |
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| 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 |
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| 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 |