The C*-algebra of the semi-direct product K and A

Abstract

Let $G=K⋉A$ be the semi-direct product group of a compact group $K$ acting on an abelian locally compact group $A$. We describe the $C^{\ast }$-algebra $C^{\ast }(G)$ of $G$ in terms of an algebra of operator fields defined over the spectrum of $G$, generalizing previous results obtained for some special classes of such groups.