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Twisted crossed products by coactions. (English) Zbl 0805.46067
Summary: We consider coactions of a locally compact group $$G$$ on a $$C^*$$-algebra $$A$$, and the associated crossed product $$C^*$$-algebra $$A\times G$$. Given a normal subgroup $$N$$ of $$G$$, we seek to decompose $$A\times G$$ as an iterated crossed product $$(A\times G/N)\times N$$, and introduce notions of twisted coaction and twisted crossed product which make this possible. We then prove a duality theorem for these twisted crossed products, and discuss how our results might be used, especially when $$N$$ is abelian.

##### MSC:
 46L55 Noncommutative dynamical systems 22D25 $$C^*$$-algebras and $$W^*$$-algebras in relation to group representations 22D35 Duality theorems for locally compact groups