Crossed Products byC0(X)-Actions
Copyright policy )Crossed Products byC0(X)-Actions
Suppose that $G$ has a representation group $H$, that $G_{ab}:= G/\bar{[G,G]}$ 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 $��\mapsto (Z_��,f_��)$ between the collection of exterior equivalence classes of locally inner actions $��:G\to\Aut(A)$, and the collection of principal $\hgab$-bundles $Z_��$ together with continuous functions $f_��:X\to H^2(G,\T)$. In this paper, we compute the crossed products $A\rtimes_��G$ in terms of the data $Z_��$, $f_��$, and~$\cs(H)$.
41 pages AMS-LaTeX -- sequel to funct-an/9706002
- Dartmouth College United States
- University of Paderborn Germany
crossed products, locally inner actions of smooth groups on \({\mathcal C}{\mathcal R}\)-algebras, primitive ideal space, Mathematics - Operator Algebras, complete regularization, Crossed products, locally inner action,C0(X)-algebras., Functional Analysis (math.FA), Mathematics - Functional Analysis, twisted group algebras, FOS: Mathematics, group \(C^*\)-algebra, Noncommutative dynamical systems, Operator Algebras (math.OA), Analysis
crossed products, locally inner actions of smooth groups on \({\mathcal C}{\mathcal R}\)-algebras, primitive ideal space, Mathematics - Operator Algebras, complete regularization, Crossed products, locally inner action,C0(X)-algebras., Functional Analysis (math.FA), Mathematics - Functional Analysis, twisted group algebras, FOS: Mathematics, group \(C^*\)-algebra, Noncommutative dynamical systems, Operator Algebras (math.OA), Analysis
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