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OverviewThe 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. Full Product DetailsAuthor: Marcelo Aguiar , Swapneel MahajanPublisher: Cambridge University Press Imprint: Cambridge University Press Dimensions: Width: 16.00cm , Height: 4.60cm , Length: 24.10cm Weight: 1.590kg ISBN: 9781009243773ISBN 10: 1009243772 Pages: 894 Publication Date: 17 November 2022 Audience: General/trade , General Format: Hardback Publisher's Status: Active Availability: In stock  We have confirmation that this item is in stock with the supplier. It will be ordered in for you and dispatched immediately. Table of ContentsIntroduction; 1. Coxeter groups and reflection arrangements; Part I. Coxeter Species: 2. Coxeter species and Coxeter bimonoids; 3. Basic theory of Coxeter bimonoids; 4. Examples of Coxeter bimonoids; 5. Coxeter operads; 6. Coxeter Lie monoids; 7. Structure theory of Coxeter bimonoids; Part II. Coxeter Spaces: 8. Coxeter spaces and Coxeter bialgebras; 9. Basic theory of Coxeter bialgebras; 10. Examples of Coxeter bialgebras; 11. Coxeter operad algebras; 12. Coxeter Lie algebras; 13. Structure theory of Coxeter bialgebras; Part III. Fock Functors: 14. Fock functors; 15. Coxeter bimonoids and Coxeter bialgebras; 16. Adjoints of Fock functors; 17. Structure theory under Fock functors; 18. Examples of Fock spaces; Appendix A. Category theory; References; List of Notations; List of Tables; List of Figures; List of Summaries; Author Index; Subject Index.ReviewsAuthor InformationMarcelo Aguiar is Professor in the Department of Mathematics at Cornell University, Ithaca. Swapneel Mahajan is Associate Professor in the Department of Mathematics at the Indian Institute of Technology, Mumbai. Tab Content 6Author Website:Countries AvailableAll regions |
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