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 - Jan 1 2019 |
Keywords
- C*-algebras
- Invertible group
- Symmetry
ASJC Scopus subject areas
- Algebra and Number Theory
- Analysis