Poisson cohomology and secondary invariants of the Poisson structure (X(2)+Y(2))(S)partial D(X) wedge partial D(Y).

摘要

The Poisson cohomology is an invariant of Poisson manifolds similar, on the one hand, to the de Rham cohomology, and on the other, to the space of vector fields for smooth manifolds. This invariant has a rich algebraic structure. In particular, the first Poisson cohomology is a Lie algebra. Its Lie algebra cohomology, whose elements we refer to as secondary invariants, gives a further refined invariant of Poisson manifolds.;We calculate the Poisson cohomology over the formal power series of the plane equipped with the Poisson structures ps=x2+y2 s6x∧6 y for all integers s ≥ 0. In addition, for s = 2, we determine the secondary invariants, namely the Lie algebra structure on the first Poisson cohomology.