Hochschild Cohomology and Quantum Diffusions.

Available from UMI in association with The British Library. Requires signed TDF. Quantum diffusions on a unital dense *-subalgebra of an algebra are defined, generalising the classical notion of diffusion on a compact differentiable manifold. Consequences of this definition are explored; in particular it is found that a necessary condition for the existence of a diffusion is that a certain Hochschild 2-cocycle be a 2-coboundary. After characterising some diffusions on unital C*-algebras, unital *-algebras with non-trivial Hochschild 2-cocycles defined on them are constructed. Extensions of these algebras are defined which are themselves unital *-algebras. Certain Hochschild 2-cocycles on the extended algebras are shown to be 2-coboundaries and explicit diffusions are computed. Finally, a possible application of the theory of quantum diffusions to a problem in solid state physics is sketched.