Tensor products of NCDL-C*-algebras and the C*-algebra of the Heisenberg motion groups

Abstract

We show that the tensor product $A\otimes B$ over $\mathbb{C}$ of two $C^{\ast }$-algebras satisfying the \textit{NCDL} conditions has again the same property. We use this result to describe the $C^{\ast }$-algebra of the Heisenberg motion groups $G_n={\mathbb{T}}^n⋉{\mathbb{H}}_n$ as algebra of operator fields defined over the spectrum of $G_n$.