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

Authors
  • Giordano, Thierry
  • Sierakowski, Adam
Type
Preprint
Publication Date
Mar 18, 2014
Submission Date
Mar 18, 2014
Identifiers
arXiv ID: 1403.4385
Source
arXiv
License
Yellow
External links

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 UCT.

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