Hochschild Cohomology and Quantum Diffusions.
Abstract
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 2cocycle be a 2coboundary. After characterising some diffusions on unital C*algebras, unital *algebras with nontrivial Hochschild 2cocycles defined on them are constructed. Extensions of these algebras are defined which are themselves unital *algebras. Certain Hochschild 2cocycles on the extended algebras are shown to be 2coboundaries and explicit diffusions are computed. Finally, a possible application of the theory of quantum diffusions to a problem in solid state physics is sketched.
 Publication:

Ph.D. Thesis
 Pub Date:
 1988
 Bibcode:
 1988PhDT........95R
 Keywords:

 Mathematics; Physics: Condensed Matter