## Abstract

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 sign_{n}(2 ≤ n ≤ ∞) and we prove that U(Script O sign_{n}) 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 language | English |
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Pages (from-to) | 1-7 |

Number of pages | 7 |

Journal | Acta Mathematica Universitatis Comenianae |

Volume | 77 |

Issue number | 1 |

Publication status | Published - Jul 1 2008 |

Externally published | Yes |

## Keywords

- Cuntz algebras
- Involutions
- K-Theory

## ASJC Scopus subject areas

- Mathematics(all)