Lie bialgebras real cohomology.
Lie-Rinehart algebras, Gerstenhaber algebras and Batalin-Vilkovisky algebras
For any Lie-Rinehart algebra , B(atalin)-V(ilkovisky) algebra structures on the exterior -algebra correspond bijectively to right -module structures on ; likewise, generators for the Gerstenhaber algebra correspond bijectively to right -connections on . When is projective as an -module, given a B-V algebra structure on , the homology of the B-V algebra coincides with the homology of with coefficients in with reference to the right -module structure determined by . When...
Losik cohomology of the Lie algebra of infinitesimal automorphisms of a -structure. II
Losik cohomology of the Lie algebra of infinitesimal automorphisms of a -structure
Matched pairs and extensions of Lie bialgebras.
Mémoire de Bertram Kostant sur les applications de la cohomologie des algèbres de Lie réductives
Modèles minimaux pour les algèbres de chaines
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.
On a new normalization for tractor covariant derivatives
A regular normal parabolic geometry of type on a manifold gives rise to sequences of invariant differential operators, known as the curved version of the BGG resolution. These sequences are constructed from the normal covariant derivative on the corresponding tractor bundle , where is the normal Cartan connection. The first operator in the sequence is overdetermined and it is well known that yields the prolongation of this operator in the homogeneous case . Our first main result...
On the classification of Moore algebras and their deformations.
On the cohomology of nilpotent Lie algebras
On the cohomology of vector fields on parallelizable manifolds
In the present paper we determine for each parallelizable smooth compact manifold the second cohomology spaces of the Lie algebra of smooth vector fields on with values in the module . The case of is of particular interest since the gauge algebra of functions on with values in a finite-dimensional simple Lie algebra has the universal central extension with center , generalizing affine Kac-Moody algebras. The second cohomology classifies twists of the semidirect product of with the...
On the Demazure character formula
Penrose's tensors. II.
Penrose's tensors on supergrassmannians.
Poisson cohomology and quantization.