Title

The general linear group as a complete invariant for C*-algebras

RIS ID

110008

Publication Details

Giordano, T. & Sierakowski, A. (2016). The general linear group as a complete invariant for C*-algebras. Journal of Operator Theory, 76 (2), 249-269.

Abstract

In 1955 Dye proved that two von Neumann factors not of type I2n are isomorphic if and only if their unitary groups are isomorphic as abstract groups. We consider an analogue for C*-algebras and show that the topological general linear group is a classifying invariant for simple unital AH-algebras of slow dimension growth and of real rank zero, and that the abstract general linear group is a classifying invariant for unital Kirchberg algebras in the UCT class.

Grant Number

ARC/DP120100389

Grant Number

ARC/DP150101598

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