Homology for operator algebras I: Spectral homology for reflexive algebras

Details Homology for operator algebras I: Spectral homology for reflexive algebras Homology for operator algebras I: Spectral homology for reflexive algebras

1994-05-18

arxiv.org/abs/funct-an/9405004v1

Mathematics

Operator Algebras

36 pages, Latex

Scientific paper

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.

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