Primitivity of unital full free products of residually finite dimensional C⁎-algebras Academic Article uri icon

abstract

  • © 2014 Elsevier Inc. A C*-algebra is called primitive if it admits a faithful and irreducible *-representation. We show that if A1 and A2 are separable, unital, residually finite dimensional C*-algebras satisfying (dim(A1)-1)(dim(A2)-1)≥2, then the unital C*-algebra full free product, A=A1*A2, is primitive. It follows that A is antiliminal, it has an uncountable family of pairwise inequivalent irreducible faithful *-representations and the set of pure states is w*-dense in the state space.

author list (cited authors)

  • Dykema, K., & Torres-Ayala, F.

citation count

  • 0

complete list of authors

  • Dykema, Ken||Torres-Ayala, Francisco

publication date

  • December 2014