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Moore Cohomology and Central Twisted Crossed Product C*-Algebras

Published online by Cambridge University Press:  20 November 2018

Judith A. Packer
Judith A. Packer*
Affiliation:
Department of Mathematics, National University of Singapore, Kent Ridge, Singapore 0511
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Abstract

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Let G be a locally compact second countable group, let X be a locally compact second countable Hausdorff space, and view C(X, T) as a trivial G-module. For G countable discrete abelian, we construct an isomorphism between the Moore cohomology group Hn (G, C(X, T)) and the direct sum Ext(H n-1(G), Ȟ l(βX, Ζ)) ⊕ C(X, Hn (G, T)); here Ȟ 1 (βX, Ζ) denotes the first Čech cohomology group of the Stone-Čech compactification of X, βX, with integer coefficients. For more general locally compact second countable groups G, we discuss the relationship between the Moore group H 2(G, C(X, T)), the set of exterior equivalence classes of element-wise inner actions of G on the stable continuous trace C*-algebra C 0(X) ⊗ 𝒦, and the equivariant Brauer group BrG (X) of Crocker, Kumjian, Raeburn, and Williams. For countable discrete abelian G acting trivially on X, we construct an isomorphism is the group of equivalence classes of principal Ĝ bundles over X first considered by Raeburn and Williams.

Keywords

46L0546L3555N9155R10

Information

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 48 , Issue 1 , 01 February 1996 , pp. 159 - 174
Copyright
Copyright © Canadian Mathematical Society 1997

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