## 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 |
---|---|

Pages (from-to) | 641-650 |

Number of pages | 10 |

Journal | Advances in Operator Theory |

Volume | 4 |

Issue number | 3 |

DOIs | |

Publication status | Published - Jan 1 2019 |

## Keywords

- C*-algebras
- Invertible group
- Symmetry

## ASJC Scopus subject areas

- Algebra and Number Theory
- Analysis