Crossed products for actions of crossed modules on C*-algebras

2013/04/24 by Buss, Alcides, Meyer, Ralf
#FOS: Mathematics #Operator Algebras (math.OA)

paper · doi:10.48550/arxiv.1304.6540

Abstract

We decompose the crossed product functor for actions of crossed modules of locally compact groups on C*-algebras into more elementary constructions: taking crossed products by group actions and fibres in C*-algebras over topological spaces. For this, we extend the theory of partial crossed products from groups to crossed modules; extend Takesaki-Takai duality to Abelian crossed modules; show that equivalent crossed modules have equivalent categories of actions on C*-algebras; and show that certain crossed modules are automatically equivalent to Abelian crossed modules.

Related

• Three versions of categorical crossed-product duality
• Crossed products of locally C*-algebras
• Crossed products of C*-algebras for singular actions
• Takai duality and crossed product hosts in C*-actions
• Structure and K-theory of crossed products by proper actions