1994/12/12 by D. Crocker, David Crocker, Alex Kumjian +7
Mathematics · #Advanced Operator Algebra Research #Advanced Topics in Algebra #FOS: Mathematics #Functional Analysis (math.FA) #Homotopy and Cohomology in Algebraic Topology #Operator Algebras (math.OA) #funct-an #math.OA
paper · pdf · doi:10.48550/arxiv.funct-an/9412002
28 pages, AMS-LaTeX v1.1
arxiv created 1994/12/12 · openalex publication_date 1994/12/12 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Suppose that (G,T) is a second countable locally compact transformation group given by a homomorphism ℓ:G→\Homeo(T), and that A is a separable continuous-trace \cs-algebra with spectrum T. An action α:G→\Aut(A) is said to cover ℓ if the induced action of G on T coincides with the original one. We prove that the set \brgt of Morita equivalence classes of such systems forms a group with multiplication given by the balanced tensor product: [A,α][B,β] = [A\Ttensor B,α\tensorβ], and we refer to \brgt as the Equivariant Brauer Group. We give a detailed analysis of the structure of \brgt in terms of the Moore cohomology of the group G and the integral cohomology of the space T. Using this, we can characterize the stable continuous-trace \cs-algebras with spectrum T which admit actions covering ℓ. In particular, we prove that if G=\R, then every stable continuous-trace \cs-algebra admits an (essentially unique) action covering~ℓ, thereby substantially improving results of Raeburn and Rosenberg. Versions of this paper in *.dvi and *.ps form are available via World wide web servers at http://coos.dartmouth.edu/~dana/dana.html