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).
|Number of pages||10|
|Journal||Advances in Operator Theory|
|Publication status||Published - Jan 1 2019|
- Invertible group
ASJC Scopus subject areas
- Algebra and Number Theory