Abelian Extensions of Quantum Logics

David J. Foulis, Richard J. Greechie

Ferdinand Chovanec, František Kôpka

Sergio Bernini

Frank Roumen

We will define two ways to assign cohomology groups to effect algebras, which occur in the algebraic study of quantum logic. The first way is based on Connes' cyclic cohomology. The resulting cohomology groups are related to the state space of the effect algebra, and can be computed using variations on the Kunneth and Mayer-Vietoris sequences. The second way involves a chain complex of ordered abelian groups, and gives rise to a cohomological characterization of state extensions on effect algebras. This has applications to no-go theorems in quantum foundations, such as Bell's theorem.

Paweł Kruszyński

David Finkelstein