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

## TL;DR

This paper characterizes the C*-algebra of a semi-direct product group formed by a compact group acting on an abelian locally compact group, extending known results to a broader class of groups.

## Contribution

It provides a general description of the C*-algebra of semi-direct product groups with compact and abelian components, generalizing earlier specific cases.

## Key findings

- Describes the C*-algebra as an algebra of operator fields over the spectrum.
- Generalizes previous results for special classes of semi-direct product groups.
- Provides a framework for analyzing the structure of C*-algebras in this context.

## Abstract

Let $G=K\ltimes A$ be the semi-direct product group of a compact group $K$ acting on an abelian locally compact group $A$. We describe the $C^*$-algebra $C^*(G)$ 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.