Groupoid Algebras Associated With Covering Maps

Abstract

For a compact Hausdorff space X with its p-fold covering map σ, we construct its corresponding topological groupoid Γ, and show that there is a strong relation between the dynamical structures of (X, σ) and the groupoid structures of Γ.

Dynamical Systems and Groupoid Algebras on Higher Rank Graphs

“…Before go further, we may need to mention that similar relations between dynamical systems and groupoids are already proved in [8] under a little different conditions.…”

“…Recall that a C * -algebra is called a prime C * -algebra if intersection of any two nonzero ideals is nonzero. 8]). Let G be a topological groupoid with open range map and G 0 its unit space.…”