Primeness and primitivity conditions for twisted group $C^*$-algebras

TL;DR

This paper establishes conditions under which twisted group $C^*$-algebras are prime or primitive, analyzing their behavior under group operations like direct and free products.

Contribution

It provides new criteria for primeness and primitivity of twisted group $C^*$-algebras and explores their stability under group product constructions.

Findings

Conditions for primeness and primitivity of twisted group $C^*$-algebras.

Behavior of these conditions under direct products of groups.

Behavior of these conditions under free products of groups.

Abstract

For a multiplier (2-cocycle) $\sigma$ on a discrete group $G$ we give conditions for which the twisted group $C^*$-algebra associated with the pair $(G,\sigma)$ is prime or primitive. We also discuss how these conditions behave on direct products and free products of groups.