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algebra g arbitrary azm+lzldz bi-vector field bzmzl calculation category of formal chain complex chapter Cocycle Condition CC Cohomology over Laurent cohomology spaces completes the proof components computation Conjugate Pairs Corollary Cq(g decomposes decomposition defined Denote differential operator direct sum element formal power series formal vector fields g-module Goncharova Theorem graded algebra homogeneous degree ideal infinite-dimensional integers invariant of Poisson isomorphic Junko Hoshi Kiinneth Kunneth formula Laurent category Laurent series Lie algebra cohomology Lie algebra structure Lie bracket Lq/L lzldz module monomial multi-vector fields namely the Lie plane R2 PMJN Poisson manifold Poisson structure Poisson structure irs primitive Proposition 1.2.6 R2 with Poisson Recall Remark Schouten-Nijenhuis bracket Second Cohomology second Poisson cohomology series with complex Serre-Hochschild Spectral Serre-Hoschild spectral sequence smooth functions space of multi-vector spectral sequence stabilizes structure constants subcomplex symplectic leaves symplectic manifold trivial vector space wedge product zszs-ldz