Hypergroup Deformations of Semigroups

TL;DR

This paper explores how hypergroup deformations can be applied to semigroups, particularly focusing on the max semigroup on non-negative integers, to understand their structure and properties.

Contribution

It introduces a framework for hypergroup deformation of max semigroups and extends the concept to general commutative semigroups through deformation on idempotents.

Findings

Hypergroup deformation of the max semigroup on non-negative integers.

Extension of hypergroup concepts to general commutative semigroups.

Insight into the structure of hypergroups arising from semigroup deformations.

Abstract

We view the well-known example of the dual of a countable compact hypergroup, motivated by the orbit space of p-adic integers by Dunkl and Ramirez (1975), as hypergroup deformation of the max semigroup structure on the linearly ordered set $\mathbb{Z}_+$ of the non-negative integers along the diagonal. This works as motivation for us to study hypergroups or semi convolution spaces arising from "max" semigroups or general commutative semigroups via hypergroup deformation on idempotents.