Non-Hausdorff Symmetries of C*-algebras

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.

very minor changes. To appear in Math. Ann

References in corpus (2)

• A higher category approach to twisted actions on C*-algebras
• 2-categorical Poincare Representations and State Sum Applications

Cited by in corpus (6)

• A higher category approach to twisted actions on C*-algebras
• A bicategorical interpretation for relative Cuntz--Pimsner algebras
• A groupoid approach to interacting fermions
• Colimits in the correspondence bicategory
• Gerbes over posets and twisted C*-dynamical systems
• Crossed module actions on continuous trace $C^{\ast }$-algebras