Coxeter Bialgebras

This monograph develops Hopf theory in the setting of a real reflection arrangement,generalizing the classical notion of a connected graded Hopf algebra. It introduces a Coxeter bialgebra and a Coxeter bimonoid,connecting them via Fock functors. This opens a new chapter in Coxeter theory and Hopf theory,relating to other areas of mathematics such as discrete geometry,semigroup theory,and category theory. It is written carefully and will be of interest to students and researchers.

Format: Hardback
Length: 894 pages
Publication date: 17 November 2022
Publisher: Cambridge University Press

This monograph aims to advance Hopf theory within the context of a real reflection arrangement, introducing a novel concept called a Coxeter bialgebra. This bialgebra serves as a generalization of the traditional notion of a connected graded Hopf algebra. The authors also introduce the notion of a Coxeter bimonoid, which provides a more structured framework. By utilizing a family of functors known as Fock functors, they establish a connection between these two notions. These Fock functors exhibit similarities with functors that connect Hopf monoids in the category of Joyal species and connected graded Hopf algebras. This monograph represents a significant milestone in both Coxeter theory and Hopf theory, fostering a strong connection between the two fields. Moreover, it exhibits fruitful connections to various other branches of mathematics, including discrete geometry, semigroup theory, associative algebras, algebraic Lie theory, operads, and category theory. The text is meticulously crafted, utilizing tables, diagrams, illustrations, and summaries to enhance understanding. It is designed to appeal to students and researchers alike, offering valuable insights and advancements in the study of these mathematical subjects.

Weight: 1592g
Dimension: 164 x 239 x 54 (mm)
ISBN-13: 9781009243773