Simplicity of q-Gaussian C*-algebras

Abstract

We show that q-Gaussian $C^{\ast }$-algebras for $q\in (-1,1)$ have the Dixmier averaging property, and hence are simple with a unique trace. We argue by combining rapid decay and spectral gap estimates for the commutators with the generators, which are obtained from free probability.

13 pages; minor edits and additional references