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

Journal Article


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.

Publication Date


  • 2016

Citation


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

Scopus Eid


  • 2-s2.0-84991264786

Ro Metadata Url


  • http://ro.uow.edu.au/eispapers/6139

Number Of Pages


  • 20

Start Page


  • 249

End Page


  • 269

Volume


  • 76

Issue


  • 2

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.

Publication Date


  • 2016

Citation


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

Scopus Eid


  • 2-s2.0-84991264786

Ro Metadata Url


  • http://ro.uow.edu.au/eispapers/6139

Number Of Pages


  • 20

Start Page


  • 249

End Page


  • 269

Volume


  • 76

Issue


  • 2