Homology for Operator Algebras

Homology for Operator Algebras II : Stable Homology for Non-self-adjoint Algebras

A new homology is defined for a non-self-adjoint operator algebra with a distinguished masa which is based upon cycles and boundaries associated with complexes of partial isometries in the stable algebra. Under natural hypotheses the zeroth order group coincides with the K0 group of the generated C ∗-algebra. Several identifications and applications are given, and in particular it is shown how ...

On the Homology Theory of Operator Algebras

For given Banach algebras A and B, we define a free resolution of algebraB over a homomorphism f : A → B and study some properties of the relative cyclic homology.

00 4 v 1 1 8 M ay 1 99 4 Homology for Operator Algebras I : Spectral homology for reflexive algebras

England 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 parti...

Operator Algebras

Notice that the left-hand side of the third equation is the sum of the left-hand sides of the first two. As a result, no solution to the system exists unless a + b = c. But if a + b = c, then any solution of the first two equations is also a solution of the third; and in any linear system involving more unknowns than equations, solutions, when they exist, are never unique. In the present case, ...

Operator Theory and Operator Algebras