School of Mathematical & Statistical Sciences Faculty Publications and Presentations

Hypergroups

Document Type

Book

Publication Date

2023

Abstract

This book provides a comprehensive algebraic treatment of hypergroups, as defined by F. Marty in 1934. It starts with structural results, which are developed along the lines of the structure theory of groups. The focus then turns to a number of concrete classes of hypergroups with small parameters, and continues with a closer look at the role of involutions (modeled after the definition of group-theoretic involutions) within the theory of hypergroups. Hypergroups generated by involutions lead to the exchange condition (a genuine generalization of the group-theoretic exchange condition), and this condition defines the so-called Coxeter hypergroups. Coxeter hypergroups can be treated in a similar way to Coxeter groups. On the other hand, their regular actions are mathematically equivalent to buildings (in the sense of Jacques Tits). A similar equivalence is discussed for twin buildings. The primary audience for the monograph will be researchers working in Algebra and/or Algebraic Combinatorics, in particular on association schemes.

Comments

Basic Facts - https://rdcu.be/eH93D

Closed Subsets - https://rdcu.be/eH93Z

Elementary Structure Theory - https://rdcu.be/eH930

Subnormality and Thin Residues - https://rdcu.be/eH932

Tight Hypergroups - https://rdcu.be/eH94f

Involutions - https://rdcu.be/eH94t

Hypergroups with a Small Number of Elements - https://rdcu.be/eH94G

Constrained Sets of Involutions - https://rdcu.be/eH95i

Coxeter Sets of Involutions - https://rdcu.be/eH95z

Regular Actions of (Twin) Coxeter Hypergroups - https://rdcu.be/eH95L

DOI

10.1007/978-3-031-39489-8

Link to Full Text

Share

COinS