Projective Modules over Graded Lie Algebras. I.
Quantization of cohomology in semi-simple Lie algebras.
Quantum dynamics on the worldvolume from classical cohomology.
Quasi-bigèbres jacobiennes
Quasi-trace functions on Lie algebras and their applications to 3-Lie algebras
We introduce the notion of quasi-trace functions on Lie algebras. As applications we study realizations of 3-dimensional and 4-dimensional 3-Lie algebras. Some comparison results on cohomologies of 3-Lie algebras and Leibniz algebras arising from quasi-trace functions are obtained.
Rapport sur les champs symplectiques formels
Representations with cohomology in the discrete spectrum of subgroups of and Lefschetz numbers
Restricted Lie algebras with bounded cohomology and related classes of algebras.
Schwarzian derivative related to modules of differential operators on a locally projective manifold
We introduce a 1-cocycle on the group of diffeomorphisms Diff(M) of a smooth manifold M endowed with a projective connection. This cocycle represents a nontrivial cohomology class of Diff(M) related to the Diff(M)-modules of second order linear differential operators on M. In the one-dimensional case, this cocycle coincides with the Schwarzian derivative, while, in the multi-dimensional case, it represents its natural and new generalization. This work is a continuation of [3] where the same problems...
Second et troisième espaces de cohomologie différentiable de l'algèbre de Lie de Poisson d'une variété symplectique
Semi-infinite cohomology and superconformal algebras
We describe representations of certain superconformal algebras in the semi-infinite Weil complex related to the loop algebra of a complex finite-dimensional Lie algebra and in the semi-infinite cohomology. We show that in the case where the Lie algebra is endowed with a non-degenerate invariant symmetric bilinear form, the relative semi-infinite cohomology of the loop algebra has a structure, which is analogous to the classical structure of the de Rham cohomology in Kähler...
Semi-infinite homological algebra.
Shapiro's lemma and its consequences in the cohomology theory of modular Lie algebras.
Singular Blocks of the Category O.
-trivial deformations of -modules of symbols.
Some remarks on the cohomology of the Poisson algebra
Spectral sequences for commutative Lie algebras
We construct some spectral sequences as tools for computing commutative cohomology of commutative Lie algebras in characteristic . In a first part, we focus on a Hochschild-Serre-type spectral sequence, while in a second part we obtain spectral sequences which compare Chevalley-Eilenberg-, commutative- and Leibniz cohomology. These methods are illustrated by a few computations.
Support varieties for restricted Lie alge-bras.
Sur la cohomologie de l'algèbre de Lie des champs de vecteurs de contact formels
Nous démontrons la finitude de la cohomologie de l’algèbre de Lie des champs de vecteurs formels à variables, respectant la forme de contact universelle .
Sur l'algebre de Lie des Champs de Vecteurs