Topological K-theory of the group C*-algebra of a semi-direct product Z^n rtimes Z/m for a free conjugation action

TL;DR

This paper calculates the topological K-theory of the reduced group C*-algebra for a specific class of semi-direct product groups where the conjugation action is free outside the origin, advancing understanding in operator algebras.

Contribution

It provides explicit computations of the topological K-theory for group C*-algebras of semi-direct products with free conjugation actions, a case not thoroughly analyzed before.

Findings

Explicit K-theory computations for Z^n rtimes Z/m groups

Extension of known results to free conjugation actions

Enhanced understanding of group C*-algebra invariants

Abstract

We compute the topological K-theory of the group C*-algebra C*_r(G) for a group extension Z^n->G->Z/m provided that the conjugation action of Z/m on Z^n is free outside the origin.