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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.

46L55 Noncommutative dynamical systems
22D25 \(C^*\)-algebras and \(W^*\)-algebras in relation to group representations
22D35 Duality theorems for locally compact groups