Journal of Noncommutative Geometry

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Volume 11, Issue 3, 2017, pp. 1195–1235
DOI: 10.4171/JNCG/11-3-12

Published online: 2017-09-26

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

Alcides Buss[1] and Ralf Meyer[2]

(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