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Type: Journal article
Title: Group actions on C*-algebras, 3-cocycles and quantum field theory
Author: Carey, Alan L.
Grundling, Hendrik B. G. S.
Raeburn, Iain
Sutherland, Colin E.
Citation: Communications in Mathematical Physics, 1995; 168(2):389-416
Publisher: Springer-Verlag
Issue Date: 1995
ISSN: 0010-3616
Statement of
A. L. Carey, H. Grundling, I. Raeburn and C. Sutherland
Abstract: We study group extensions Δ→Γ→Ω, where Γ acts on a C*-algebra A. Given a twisted covariant representation π, V of the pair A, Δ we construct 3-cocycles on Ω with values in the centre of the group generated by V(Δ). These 3-cocycles are obstructions to the existence of an extension of Ω by V(Δ) which acts on A compatibly with Γ. The main theorems of the paper introduce a subsidiary invariant Λ which classifies actions of Γ on V(Δ) and in terms of which a necessary and sufficient condition for the the cohomology class of the 3-cocycle to be non-trivial may be formulated. Examples are provided which show how non-trivial 3-cocycles may be realised. The framework we choose to exhibit these essentially mathematical results is influenced by anomalous gauge field theories. We show how to interpret our results in that setting in two ways, one motivated by an algebraic approach to constrained dynamics and the other by the descent equation approach to constructing cocycles on gauge groups. In order to make comparisons with the usual approach to cohomology in gauge theory we conclude with a Lie algebra version of the invariant Λ and the 3-cocycle.
DOI: 10.1007/BF02101555
Appears in Collections:Pure Mathematics publications

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