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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...
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...
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.
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 .
Some of the completely integrable Hamiltonian systems obtained through Adler-Kostant-Symes theorem rely on two distinct Lie algebra structures on the same underlying vector space. We study here the cases when two structures are linked together by deformations.
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