Graded C*-algebras and twisted groupoid C*-algebras

摘要

Let A be C*-algebra that is acted upon by a compact abelian group. We show that if the fixed-point algebra of the action contains a Cartan subalgebra D satisfying an appropriate regularity condition, then A is the reduced C*-algebra of a groupoid twist. We further show that the embedding D ? A is uniquely determined by the twist. These results generalize Renault's results on Cartan subalgebras of C*-algebras.