Non-isomorphic C*-algebras with isomorphic unitary groups

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1 Citation (Scopus)


Dye, [Ann. of Math. (2) 61 (1955), 73-89] proved that the discrete unitary group in a factor determines the algebraic type of the factor. Afterwards, for a large class of simple unital C*-algebras, Al-Rawashdeh, Booth and Giordano [J. Funct. Anal. 262 (2012), 4711-4730] proved that the algebras are *-isomorphic if and only if their unitary groups are isomorphic as abstract groups. In this paper, we give a counterexample in the non-simple case. Indeed, we give two C*-algebras with isomorphic unitary groups but the algebras themselves are not *-isomorphic.

Original languageEnglish
Pages (from-to)160-163
Number of pages4
JournalAdvances in Operator Theory
Issue number2
Publication statusPublished - Sept 1 2016
Externally publishedYes


  • *-isomorphism
  • C*-algebra
  • Unitary group

ASJC Scopus subject areas

  • Analysis
  • Algebra and Number Theory


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