Non-Hausdorff Symmetries of C*-algebras

TL;DR

This paper explores the symmetries of C*-algebras linked to non-Hausdorff spaces, introducing a framework using crossed modules of groupoids to define actions and crossed products, supported by foundational results and examples.

Contribution

It introduces a novel approach to describe non-Hausdorff symmetries of C*-algebras via crossed modules of groupoids, including new definitions and basic properties.

Findings

Defined actions of crossed modules on C*-algebras

Established crossed product constructions for these actions

Provided examples illustrating the concepts

Abstract

Symmetry groups or groupoids of C*-algebras associated to non-Hausdorff spaces are often non-Hausdorff as well. We describe such symmetries using crossed modules of groupoids. We define actions of crossed modules on C*-algebras and crossed products for such actions, and justify these definitions with some basic general results and examples.