Nilpotent cohomology of the oscillator representation.
Nondegenerate cohomology pairing for transitive Lie algebroids, characterization
The Evens-Lu-Weinstein representation (Q A, D) for a Lie algebroid A on a manifold M is studied in the transitive case. To consider at the same time non-oriented manifolds as well, this representation is slightly modified to (Q Aor, Dor) by tensoring by orientation flat line bundle, Q Aor=QA⊗or (M) and D or=D⊗∂Aor. It is shown that the induced cohomology pairing is nondegenerate and that the representation (Q Aor, Dor) is the unique (up to isomorphy) line representation for which the top group of...
Non-degenerescence of some spectral sequences
Each Lie algebra of vector fields (e.g. those which are tangent to a foliation) of a smooth manifold définies, in a natural way, a spectral sequence which converges to the de Rham cohomology of in a finite number of steps. We prove e.g. that for all there exists a foliated compact manifold with infinite dimensional.
Non-Hamiltonian actions and Lie-algebra cohomology of vector fields.
Nonsplit extensions of modular Lie algebras of rank 2.