Connes' metric for states in group algebras
Loading...
Date
Authors
Journal Title
Journal ISSN
Volume Title
Publisher
Abstract
Description
In this article we follow the main idea of A. Connes for the construction of a metric in the state space of a C*-algebra. We focus in the reduced algebra of a discrete group $Γ$, and prove some equivalences and relations between two central objects of this category: the word-length growth (connected with the degree of the extension of $Γ$ when the group is an extension of Z by a finite group), and the topological equivalence between the w*-topology and the one introduced with this metric in the state space of $C_r*(Γ)$.