A note on ideal spaces of Mautner groups

TL;DR

This paper investigates the structure of the $C^*$-algebras associated with 5-dimensional Mautner groups, revealing their quasi-standard nature and detailing the topology of their ideal spaces.

Contribution

It provides the first detailed analysis of the ideal space topology for $C^*$-algebras of Mautner groups, highlighting their quasi-standard property.

Findings

Mautner group $C^*$-algebras are quasi-standard.

Topology of minimal primal and Glimm ideal spaces is described.

Mautner groups have non-type-I factor representations.

Abstract

The Mautner groups are the 5-dimensional solvable Lie groups that have non-type-I factor representations. We show that their corresponding group $C^*$-algebras are quasi-standard and we describe the topology of their spaces of minimal primal ideals and Glimm ideals.