Classifying the Type of Principal Groupoid C*-algebras

الأصل · EN

Suppose G is a second countable, locally compact, Hausdorff groupoid with a fixed left Haar system. Let /G denote the orbit space of G and (G) denote the groupoid C*-algebra. Suppose that G is a principal groupoid. We show that C*(G) is CCR if and only if /G is a T₁ topological space, and that C*(G) is GCR if and only if /G is a T₀ topological space. We also show that C*(G) is a Fell Algebra if and only if G is a Cartan groupoid.