Geometry of Poisson structures.
Giunashvili, Z. (1995)
Georgian Mathematical Journal
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Giunashvili, Z. (1995)
Georgian Mathematical Journal
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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.
Manea, Adelina (2005)
General Mathematics
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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. ...
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.
Neumaier, Nikolai, Waldmann, Stefan (2009)
SIGMA. Symmetry, Integrability and Geometry: Methods and Applications [electronic only]
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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.
Kostadin Trenčevski (2003)
Kragujevac Journal of Mathematics
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Yuly Billig, Karl-Hermann Neeb (2008)
Annales de l’institut Fourier
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In the present paper we determine for each parallelizable smooth compact manifold the second cohomology spaces of the Lie algebra of smooth vector fields on with values in the module . The case of is of particular interest since the gauge algebra of functions on with values in a finite-dimensional simple Lie algebra has the universal central extension with center , generalizing affine Kac-Moody algebras. The second cohomology classifies twists of the semidirect product...