## Abstract

In simple unital purely infinite C*-algebra A, Leen proved that any element in the identity component of the invertible group is a finite product of symmetries of A. Revising Leen's factorization, we show that a multiple of eight of such factors are *-symmetries of the form 1-2P _{i,j} (u), where P _{i,j} (u) are certain projections of the C*-matrix algebra, defined by Dye as P _{i,j} (u) = 1/2 (e _{i,i} + e _{j,j} + e _{i,1} ue _{1,j} + e _{j,1} u*e _{1,i} ); for a given system of matrix units (e _{i,j} ) _{i,j=1} ^{n} of A and a unitary u ∈ U(A).

Original language | English |
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Pages (from-to) | 641-650 |

Number of pages | 10 |

Journal | Advances in Operator Theory |

Volume | 4 |

Issue number | 3 |

DOIs | |

Publication status | Published - 2019 |

## Keywords

- C*-algebras
- Invertible group
- Symmetry

## ASJC Scopus subject areas

- Analysis
- Algebra and Number Theory