Displaying similar documents to “Several cohomology algebras connected with Poisson structure.”

Associative and Lie deformations of Poisson algebras

Elisabeth Remm (2012)

Communications in Mathematics

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Considering a Poisson algebra as a nonassociative algebra satisfying the Markl-Remm identity, we study deformations of Poisson algebras as deformations of this nonassociative algebra. We give a natural interpretation of deformations which preserve the underlying associative structure and of deformations which preserve the underlying Lie algebra and we compare the associated cohomologies with the Poisson cohomology parametrizing the general deformations of Poisson algebras.

Geometry of third order ODE systems

Alexandr Medvedev (2010)

Archivum Mathematicum

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We compute cohomology spaces of Lie algebras that describe differential invariants of third order ordinary differential equations. We prove that the algebra of all differential invariants is generated by 2 tensorial invariants of order 2, one invariant of order 3 and one invariant of order 4. The main computational tool is a Serre-Hochschild spectral sequence and the representation theory of semisimple Lie algebras. We compute differential invariants up to degree 2 as application. ...

Some Remarks on Dirac Structures and Poisson Reductions

Zhang-Ju Liu (2000)

Banach Center Publications

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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.

The BV-algebra of a Jacobi manifold

Izu Vaisman (2000)

Annales Polonici Mathematici

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We show that the Gerstenhaber algebra of the 1-jet Lie algebroid of a Jacobi manifold has a canonical exact generator, and discuss duality between its homology and the Lie algebroid cohomology. We also give new examples of Lie bialgebroids over Poisson manifolds.