Crossed products by $C_0(X)$-actions

Abstract

Suppose that $G$ has a representation group $H$, that $G_{ab}:=G/\overline{[G,G]}$ is compactly generated, and that $A$ is a \cs-algebra for which the complete regularization of $\Prim(A)$ is a locally compact Hausdorff space $X$. In a previous article, we showed that there is a bijection $\alpha \mapsto (Z_{\alpha },f_{\alpha })$ between the collection of exterior equivalence classes of locally inner actions $α:G\to\Aut(A)$, and the collection of principal $\hgab$-bundles $Z_{\alpha }$ together with continuous functions $f_α:X\to H^2(G,\T)$. In this paper, we compute the crossed products $A{⋊}_{\alpha }G$ in terms of the data $Z_{\alpha }$, $f_{\alpha }$, and~$\cs(H)$.

41 pages AMS-LaTeX -- sequel to funct-an/9706002

References in corpus (1)

• Tensor products of C(X)-algebras over C(X)

Cited by in corpus (3)

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• Norms of inner derivations for multiplier algebras of C*-algebras and group C*-algebras, II
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