| If G is a real Lie group that is either nilpotent or simply connected solvable, and D (L-HOOK) G is a discrete co-compact subgroup, classical results of Van Est and Mostow imply that the cohomology of the real Lie algebra of right-invariant vector fields on G with trivial (//R)-coefficients is isomorphic to the real singular cohomology of the homogeneous space G/D. Priddy and Lambe have extended this isomorphism for nilmanifolds to the case of trivial (,r)-coefficients, (,r) = {lcub}1/2,...,1/r{rcub}. In Chapter I we work on the related problem of finding torsion elements in the integral cohomology of the Lie algebra associated to the unipotent group of strict upper triangular matrices. In Chapter II we extend the results of Priddy and Lambe to certain local coefficient systems on nilmanifolds. In Chapter III we work with algebraic groups G over and develop a sheaf-theoretic construction to relate the -cohomology of the algebraic Lie algebra L G of G to the singular -cohomology of certain homogeneous spaces that may be associated to G . |
