Semigroup C*-algebras arising from graphs of monoids

TL;DR

This paper investigates the structure and properties of semigroup C*-algebras derived from graphs of monoids within the framework of right LCM monoids, providing new criteria and detailed analysis.

Contribution

It establishes a general criterion for when a graph of monoids yields a right LCM submonoid of the fundamental group and analyzes the structural properties of the resulting C*-algebras.

Findings

Characterization of right LCM submonoids from graphs of monoids

Analysis of ideal structure and nuclearity of the C*-algebras

Construction of non-conjugate Cartan subalgebras in Kirchberg algebras

Abstract

We study groupoids and semigroup C*-algebras arising from graphs of monoids, in the setting of right LCM monoids. First, we establish a general criterion when a graph of monoids gives rise to a submonoid of the fundamental group which is right LCM. Moreover, we carry out a detailed analysis of structural properties of semigroup C*-algebras arising from graphs of monoids, including closed invariant subspaces and topological freeness of the groupoids as well as ideal structure, nuclearity and K-theory of the semigroup C*-algebras. As an application, we construct families of pairwise non-conjugate Cartan subalgebras in every UCT Kirchberg algebra.