NON-HAUSDORFF E'TALE GROUPOIDS AND THEIR C*-ALGEBRAS

In this paper we will study the basic facts about etale groupoids and their associated C*-algebras. If C*(Γ) is the C*-algebras associated to the groupoid Γ, we will show that C*(Γ) admits a per-grading over an inverse semigroup S. Also, we will prove thet C*(Γ) is naturally isomorphic to the inuerse semigroup crossed product, C0(X)*αS.

Keywords:

C*-algebras , representation , groupiod , semigroup