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.
| ISBN: | 9781009243773 |
| Publication date: | 17th November 2022 |
| Author: | Marcelo Aguiar, Swapneel Arvind Mahajan |
| Publisher: | Cambridge University Press |
| Format: | Hardback |
| Pagination: | 894 pages |
| Series: | Encyclopedia of Mathematics and Its Applications |
| Genres: |
Algebra |
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 Bialgebras features in the following genres: Algebra, Combinatorics and graph theory
Coxeter Bialgebras is available in Hardback
Coxeter Bialgebras was written by Marcelo Aguiar, Swapneel Arvind Mahajan and published by Cambridge University Press
Coxeter Bialgebras has 894 pages
Yes it is part of Encyclopedia of Mathematics and Its Applications series
£127.80