Connes' metric for states in group algebras

Details Connes' metric for states in group algebras Connes' metric for states in group algebras

2008-05-18

arxiv.org/abs/0805.2732v1

Mathematics

Operator Algebras

Scientific paper

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 $\Gamma$, 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 $\Gamma$ 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 $C_r*(\Gamma)$.

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