Normal generation of unitary groups of Cuntz algebras by involutions

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In purely infinite factors, P. de la Harpe proved that a normal subgroup of the unitary group which contains a non-trivial self-adjoint unitary contains all self-adjoint unitaries of the factor. Also he proved the same result in finite continuous factors. In a previous work the author proved a similar result in some types of unital AF-algebras. In this paper we extend the result of de la Harpe, concerning the purely infinite factors to a main example of purely infinite C*-algebras called the Cuntz algebras Script O signn(2 ≤ n ≤ ∞) and we prove that U(Script O signn) is normally generated by some non-trivial involution. In particular, in the Cuntz algebra Script O sign we prove that U(Script O sign) is normally generated by self-adjoint unitary of odd type.

Original languageEnglish
Pages (from-to)1-7
Number of pages7
JournalActa Mathematica Universitatis Comenianae
Issue number1
Publication statusPublished - 2008
Externally publishedYes


  • Cuntz algebras
  • Involutions
  • K-Theory

ASJC Scopus subject areas

  • General Mathematics


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