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On the Lichnerowicz-Poisson cohomology complex and quasi-Poisson algebras
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This article explores F-commutative algebra (A,·) with Poisson structure defined by a non-Lie algebra bivector Q. We analyse the Lichnerowicz-Poisson coboundary δ*Q and its implications as a quasi-Poisson structure, where the Schouten bracket does not vanish, complicating cohomology computations. The examined open question is whether the deviating term is a coboundary of Poisson cohomology. Our main objectives are to construct a Poisson subalgebra on which the twisted term δ2Q(Q) vanishes, and to study the existence of Poisson structures P on a Poisson ideal satisfying the condition δ2P(·) = δ2Q(Q).
Title: On the Lichnerowicz-Poisson cohomology complex and quasi-Poisson algebras
Description:
This article explores F-commutative algebra (A,·) with Poisson structure defined by a non-Lie algebra bivector Q.
We analyse the Lichnerowicz-Poisson coboundary δ*Q and its implications as a quasi-Poisson structure, where the Schouten bracket does not vanish, complicating cohomology computations.
The examined open question is whether the deviating term is a coboundary of Poisson cohomology.
Our main objectives are to construct a Poisson subalgebra on which the twisted term δ2Q(Q) vanishes, and to study the existence of Poisson structures P on a Poisson ideal satisfying the condition δ2P(·) = δ2Q(Q).
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