On étudie la cohomologie de Chevalley de la représentation adjointe de l’algèbre de Poisson d’une variété symplectique. On obtient en particulier une description explicite de la cohomologie des cochaînes 2 et 3-différentiables.
We introduce a new cohomology for Lie algebroids, and prove that it provides a differential graded Lie algebra which “controls” deformations of the structure bracket of the algebroid.
The purpose of this paper is to establish a connection between various objects such as dynamical -matrices, Lie bialgebroids, and Lagrangian subalgebras. Our method relies on the theory of Dirac structures and Courant algebroids. In particular, we give a new method of classifying dynamical -matrices of simple Lie algebras , and prove that dynamical -matrices are in one-one correspondence with certain Lagrangian subalgebras of .
In 2001, B. Malgrange defines the D-envelope or galoisian envelope of an analytical dynamical system. Roughly speaking, this is the algebraic hull of the dynamical system. In this short article, the D-envelope of a rational map R: P1 --> P1 is computed. The rational maps characterised by a finitness property of their D-envelope appear to be the integrable ones.