1997/06/17 by Siegfried Echterhoff, Echterhoff, Siegfried, Dana P. Williams +1 · 1 citation
Mathematics · #Advanced Operator Algebra Research #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Functional Analysis (math.FA) #Operator Algebras (math.OA) #funct-an #math.OA
paper · pdf · doi:10.48550/arxiv.funct-an/9706002
33 pages AMS-LaTeX
arxiv created 1997/06/17 · openalex publication_date 1997/06/17 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 H1(X,\sheaf Gab) ⊕ C(X,H2(G,\T)). As a consequence, we can compute the equivariant Brauer group \BrG(X) for G acting trivially on X.