Regular actions of Coxeter hypergroups
Christopher French, Paul-Hermann Zieschang · Communications in Algebra · 2023
Generalizing the notion of a group action, we define actions of hypergroups. Our focus is on regular actions. In contrast to groups which always allow exactly one (right) regular action hypergroups may have no regular action, they also may have infinitely many regular actions. With an eye on the second case we establish a class of hypergroups the regular actions of which correspond in a bijective way to semiregular buildings. (The class of semiregular buildings includes the class of thick buildings and is defined via a regularity condition on the panels of a building.)