Locally Inner Actions on C 0 (x)-algebras
نویسنده
چکیده
We make a detailed study of locally inner actions on C∗-algebras whose primitive ideal spaces have locally compact Hausdorff complete regularizations. We suppose that G has a representation group and compactly generated abelianization Gab. Then if the complete regularization of Prim(A) is X , we show that the collection of exterior equivalence classes of locally inner actions of G on A is parameterized by the group EG(X) of exterior equivalence classes of C0(X)-actions of G on C0(X,K). Furthermore, we exhibit a group isomorphism of EG(X) with the direct sum H(X, Ĝab) ⊕ C ( X,H(G,T) ) . As a consequence, we can compute the equivariant Brauer group BrG(X) for G acting trivially on X .
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