On certain projections of c*-matrix algebras

Research output: Contribution to journalArticlepeer-review

4 Citations (Scopus)


In 1955, H. Dye defined certain projections of a C*-matrix algebraby [formula] which was used to show that in the case of factors not of type I2n, the unitarygroup determines the algebraic type of that factor. We study these projectionsand we show that in M2(C), the set of such projections includes all the projections. For infinite C*-algebra A, having a system of matrix units, we haveA ≃ Mn(A). M. Leen proved that in a simple, purely infinite C*-algebra A, the *-symmetries generate u0(A). Assuming K1(A) is trivial, we revise Leen’sproof and we use the same construction to show that any unitary close to theunity can be written as a product of eleven *-symmetries, eight of such are ofthe form 1 − 2Pi, j (ω), ω ∈ u (A). In simple, unital purely infinite C*-algebrashaving trivial K1-group, we prove that all Pi, j (ω) have trivial K0-class. Consequently, we prove that every unitary of On can be written as a finite productof *-symmetries, of which a multiple of eight are conjugate as group elements.

Original languageEnglish
Pages (from-to)144-154
Number of pages11
JournalAnnals of Functional Analysis
Issue number2
Publication statusPublished - 2012


  • C*-algebras
  • K-class
  • Matrix projection

ASJC Scopus subject areas

  • Analysis
  • Anatomy
  • Algebra and Number Theory


Dive into the research topics of 'On certain projections of c*-matrix algebras'. Together they form a unique fingerprint.

Cite this