Unitary groups as a complete invariant

Ahmed Al-Rawashdeh, Andrew Booth, Thierry Giordano

Research output: Contribution to journalArticlepeer-review

14 Citations (Scopus)


Dye proved that the discrete unitary group in a factor determines the algebraic type of the factor. We show that if the unitary groups of two simple unital AH-algebras of slow dimension growth and of real rank zero are isomorphic as abstract groups, then their K 0-ordered groups are isomorphic. Also, using Gong and Dadarlat's classification theorem, we prove that such C *-algebras are isomorphic if and only if their unitary groups are isomorphic as topological groups. For simple, unital purely infinite C *-algebras, we show that two unital Kirchberg algebras are *-isomorphic if and only if their unitary groups are isomorphic as abstract groups.

Original languageEnglish
Pages (from-to)4711-4730
Number of pages20
JournalJournal of Functional Analysis
Issue number11
Publication statusPublished - Jun 1 2012


  • C -algebras
  • K-theory
  • Unitary groups

ASJC Scopus subject areas

  • Analysis


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