Representing Structured Semigroups on Etale Groupoid Bundles

TL;DR

This paper extends the Kumjian-Renault representation of C*-algebras to semigroups, demonstrating how to represent semigroups with special subsemigroups as slice-sections of groupoid bundles, advancing the understanding of algebraic structures in operator algebras.

Contribution

It introduces a novel representation of semigroups with normal subsemigroups via groupoid bundles, generalizing existing frameworks for C*-algebras.

Findings

Representation of semigroups as slice-sections of groupoid bundles

Extension of Kumjian-Renault representation to semigroup context

Framework for analyzing semigroup structures in operator algebras

Abstract

We examine a semigroup analogue of the Kumjian-Renault representation of C*-algebras with Cartan subalgebras on twisted groupoids. Specifically, we show how to represent semigroups with distinguished normal subsemigroups as `slice-sections' of groupoid bundles.