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

Research output: Contribution to journalJournal article

Published

Journal publication date1995
JournalJournal of Functional Analysis
Journal number1
Volume131
Number of pages25
Pages29-53
Original languageEnglish

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.