Semigroup C*-algebras arising from graphs of monoids

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.

32 pages; final version (minor changes), accepted for publication in Int. Math. Res. Not

References in corpus (2)

• Ideal structure and pure infiniteness of ample groupoid $C^{\ast }$-algebras
• C*-algebras associated to graphs of groups