Actions of Finite Hypergroups
نویسنده
چکیده
This paper is concerned with actions of finite hypergroups on sets. After introducing the definitions in the first section, we use the notion of ‘maximal actions’ to characterise those hypergroups which arise from association schemes, introduce the natural sub-class of *-actions of a hypergroup and introduce a geometric condition for the existence of *-actions of a Hermitian hypergroup. Following an insightful suggestion of Eiichi Bannai we obtain an example of the surprising phenomenon of a 3-element hypergroup with infinitely many pairwise inequivalent irreducible *-actions.
منابع مشابه
On maximal actions and w-maximal actions of finite hypergroups
Sunder and Wildberger (J. Algebr. Comb. 18, 135–151, 2003) introduced the notion of actions of finite hypergroups, and studied maximal irreducible actions and *-actions. One of the main results of Sunder and Wildberger states that if a finite hypergroup K admits an irreducible action which is both a maximal action and a *action, then K arises from an association scheme. In this paper we will fi...
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