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Schwarzian derivative related to modules of differential operators on a locally projective manifold

S. Bouarroudj, V. Ovsienko (2000)

Banach Center Publications

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...

Some division theorems for vector fields

Andrzej Zajtz (1993)

Annales Polonici Mathematici

This paper is concerned with the problem of divisibility of vector fields with respect to the Lie bracket [X,Y]. We deal with the local divisibility. The methods used are based on various estimates, in particular those concerning prolongations of dynamical systems. A generalization to polynomials of the adjoint operator (X) is given.

Some Remarks on Dirac Structures and Poisson Reductions

Zhang-Ju Liu (2000)

Banach Center Publications

Dirac structures are characterized in terms of their characteristic pairs defined in this note and then Poisson reductions are discussed from the point of view of Dirac structures.

Subalgebras of finite codimension in symplectic Lie algebra

Mohammed Benalili, Abdelkader Boucherif (1999)

Archivum Mathematicum

Subalgebras of germs of vector fields leaving 0 fixed in R 2 n , of finite codimension in symplectic Lie algebra contain the ideal of germs infinitely flat at 0 . We give an application.

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