University of Wollongong
Browse

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

journal contribution
posted on 2024-11-16, 04:08 authored by Thierry Giordano, Adam Sierakowski
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.

Funding

Cohomology, symbolic dynamics and operator algebras

Australian Research Council

Find out more...

Groupoids as bridges between algebra and analysis

Australian Research Council

Find out more...

History

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.

Journal title

Journal of Operator Theory

Volume

76

Issue

2

Pagination

249-269

Language

English

RIS ID

110008

Usage metrics

    Categories

    Keywords

    Exports

    RefWorks
    BibTeX
    Ref. manager
    Endnote
    DataCite
    NLM
    DC