Non-K-exact uniform Roe C*-algebras

TL;DR

This paper demonstrates that certain uniform Roe C*-algebras derived from expander graphs associated with groups having property ( au) are not K-exact, highlighting limitations in their algebraic structure.

Contribution

It establishes the non-K-exactness of uniform Roe C*-algebras for specific expanders from groups with property ( au), including Cayley graphs of alternating groups.

Findings

Uniform Roe C*-algebras from some expanders are not K-exact.

Expander graphs from groups with property ( au) exhibit this non-K-exactness.

Cayley graphs of alternating groups serve as key examples.

Abstract

We prove that uniform Roe C*-algebras associated to some expander graphs coming from discrete groups with property (\tau) are not K-exact. In particular, we show that this is the case for the expander obtained as Cayley graphs of a sequence of alternating groups (with appropriately chosen generating sets).