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Homology for operator algebras I: spectral homology for reflexive algebras.

Power, S. C. (1995) Homology for operator algebras I: spectral homology for reflexive algebras. Journal of Functional Analysis, 131 (1). pp. 29-53.

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Abstract

A stable homology theory is defined for completely distributive CSL algebras in terms of the point-neighbourhood homology of the partially ordered set of meet-irreducible elements of the invariant projection lattice. This specialises to the simplicial homology of the underlying simplicial complex in the case of a digraph algebra. These groups are computable and useful. In particular it is shown that if the first spectral homology group is trivial then Schur automorphisms are automatically quasispatial. This motivates the introduction of essential Hochschild cohomology which we define by using the point weak star closure of coboundaries in place of the usual coboundaries.

Item Type: Article
Journal or Publication Title: Journal of Functional Analysis
Subjects: Q Science > QA Mathematics
Departments: Faculty of Science and Technology > Mathematics and Statistics
ID Code: 19592
Deposited By: ep_ss_importer
Deposited On: 13 Nov 2008 11:26
Refereed?: Yes
Published?: Published
Last Modified: 09 Oct 2013 13:12
Identification Number:
URI: http://eprints.lancs.ac.uk/id/eprint/19592

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