Coxeter Bialgebras
Part of Encyclopedia of Mathematics and its Applications
- Authors:
- Marcelo Aguiar, Cornell University, Ithaca
- Swapneel Mahajan, Indian Institute of Technology, Mumbai
- Date Published: November 2022
- availability: Available
- format: Hardback
- isbn: 9781009243773
Hardback
Other available formats:
eBook
Looking for an inspection copy?
Please email [email protected] to enquire about an inspection copy of this book
-
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.
Read more- Readers get to learn a theory first hand from its original creators
- Carefully designed chapters, with effective use of tables, diagrams, summaries, worked examples, and exercises with hints
- Touches many different areas of mathematics with minimum prerequisites so readers can choose entry points depending on their background and interest
- Suitable for use as a course textbook, or to run a seminar, or for self-study
Customer reviews
Not yet reviewed
Be the first to review
Review was not posted due to profanity
×Product details
- Date Published: November 2022
- format: Hardback
- isbn: 9781009243773
- length: 894 pages
- dimensions: 241 x 160 x 46 mm
- weight: 1.59kg
- availability: Available
Table of Contents
Introduction
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.
Related Books
related journals
Sorry, this resource is locked
Please register or sign in to request access. If you are having problems accessing these resources please email [email protected]
Register Sign in» Proceed
You are now leaving the Cambridge University Press website. Your eBook purchase and download will be completed by our partner www.ebooks.com. Please see the permission section of the www.ebooks.com catalogue page for details of the print & copy limits on our eBooks.
Continue ×Are you sure you want to delete your account?
This cannot be undone.
Thank you for your feedback which will help us improve our service.
If you requested a response, we will make sure to get back to you shortly.
×