When amenable groups have real rank zero $C^*$-algebras

Iason Moutzouris

When amenable groups have real rank zero $C^*$-algebras

Operator Algebras 2023-10-03 v3 Group Theory

Authors: Iason Moutzouris

Abstract

We investigate when discrete, amenable groups have $C^*$ -algebras of real rank zero. While it is known that this happens when the group is locally finite, the converse in an open problem. We show that if $C^*(G)$ has real rank zero, then all normal subgroups of $G$ that are elementary amenable and have finite Hirsch length must be locally finite.

Keywords

c*-algebras amenable groups cuntz semigroup

Cite

@article{arxiv.2306.07231,
  title  = {When amenable groups have real rank zero $C^*$-algebras},
  author = {Iason Moutzouris},
  journal= {arXiv preprint arXiv:2306.07231},
  year   = {2023}
}

Comments

13 pages, corrections made from previous version (including ones based on referee's comments). To appear on the International Journal of Mathematics

Related papers

View all related →