Bundles of Generalized Fixed-Point Algebras for Proper Groupoid Dynamical Systems

TL;DR

This paper demonstrates that generalized fixed-point algebras in proper groupoid dynamical systems can be fibered over any suitable locally compact Hausdorff space, expanding understanding of their structure and applications.

Contribution

It introduces a method to fiber generalized fixed-point algebras over arbitrary locally compact Hausdorff spaces in proper groupoid dynamical systems.

Findings

Fixed-point algebra can be fibered over any locally compact Hausdorff space with a continuous map.

Provides key examples illustrating the fibered structure.

Expands the theoretical framework for proper groupoid dynamical systems.

Abstract

In this paper, we show that the generalized fixed-point algebra of a proper groupoid dynamical system, under certain assumptions, may be fibered over any locally compact Hausdorff space to which a continuous map exists from the unit space of the underlying groupoid. We will also provide some important examples.