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

TL;DR

This paper demonstrates that the tensor product of two NCDL-C*-algebras retains the NCDL property and applies this to describe the C*-algebra of Heisenberg motion groups as operator fields over their spectrum.

Contribution

It establishes the stability of the NCDL property under tensor products and characterizes the C*-algebra of Heisenberg motion groups in this framework.

Findings

Tensor product of NCDL-C*-algebras remains NCDL.

C*-algebra of Heisenberg motion groups described as operator fields.

Provides a structural understanding of these C*-algebras.

Abstract

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