The crossed-product structure of C*-algebras arising from topological dynamical systems

TL;DR

This paper demonstrates that certain topological k-graph C*-algebras can be represented as semigroup crossed products, linking topological dynamics with operator algebra structures.

Contribution

It establishes a realization of topological k-graph C*-algebras as semigroup crossed products under specific conditions, expanding the understanding of their algebraic structure.

Findings

Topological k-graph C*-algebras are realizable as semigroup crossed products.

The construction applies to locally compact Hausdorff spaces with commuting local homeomorphisms.

A uniform boundedness condition on inverse image cardinalities is essential.

Abstract

We show that every topological k-graph constructed from a locally compact Hausdorff space {\Omega} and a family of pairwise commuting local homeomorphisms on {\Omega} satisfying a uniform boundedness condition on the cardinalities of inverse images may be realized as a semigroup crossed product in the sense of Larsen.