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arXiv · 1403.4385

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

Thierry Giordano·Adam Sierakowski
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Abstract

In 1955 Dye proved that two von Neumann factors not of type I_2n are isomorphic (via a linear or a conjugate linear *-isomorphism) if and only if their unitary groups are isomorphic as abstract groups. We consider an analogue for C*-algebras. We 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 the abstract general linear group is a classifying invariant for unital Kirchberg algebras in the UCT class.

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Thierry Giordano, Adam Sierakowski. 2014-03-18. The general linear group as a complete invariant for C*-algebras. https://arxiv.org/abs/1403.4385

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