Journal of Noncommutative Geometry
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Published online: 2017-09-26
Crossed products for actions of crossed modules on C*-algebrasAlcides Buss and Ralf Meyer (1) Universidade Federal de Santa Catarina, Florianópolis, Brazil
(2) Universität Göttingen, Germany
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 Takesaki–Takai duality to Abelian crossed modules; describe the crossed product for an extension of 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.
Keywords: C*-algebra, crossed module, Fell bundle, Takesaki–Takai duality
Buss Alcides, Meyer Ralf: Crossed products for actions of crossed modules on C*-algebras. J. Noncommut. Geom. 11 (2017), 1195-1235. doi: 10.4171/JNCG/11-3-12