C*-algebras associated to topological Ore semigroups

Abstract

Let $G$ be a locally compact group and $P\subset G$ be a closed Ore semigroup containing the identity element. Let $V: P \to B(\clh)$ be a representation such that for every $a\in P$, $V_a$ is an isometry and the final projections of $\{V_a:a\in P\}$ commute. In this article, we study the $C^{\ast }$-algebra ${\mathcal{W}}_V(P,G)$, generated by $\{\int f(a)V_{a}da:f\in L^1(P)\}$. We show that there exists a universal $C^{\ast }$-algebra, which admits a groupoid description, of which ${\mathcal{W}}_V(P,G)$ is a quotient. If $P=G$, then this universal algebra is just $C^{\ast }(G)$.

References in corpus (1)

• Groupoids associated to semigroup actions

Cited by in corpus (1)

• CCR flows associated to closed convex cones