0000000000014417

AUTHOR

A. M. Perelomov

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The Schouten - Nijenhuis bracket, cohomology and generalized Poisson structures

1996

Newly introduced generalized Poisson structures based on suitable skew-symmetric contravariant tensors of even order are discussed in terms of the Schouten-Nijenhuis bracket. The associated `Jacobi identities' are expressed as conditions on these tensors, the cohomological contents of which is given. In particular, we determine the linear generalized Poisson structures which can be constructed on the dual spaces of simple Lie algebras.

High Energy Physics - TheoryMathematics - Differential GeometryPhysicsPure mathematicsSchouten–Nijenhuis bracketFOS: Physical sciencesGeneral Physics and AstronomyOrder (ring theory)Statistical and Nonlinear PhysicsPoisson distributionCohomologysymbols.namesakeBracket (mathematics)High Energy Physics - Theory (hep-th)Differential Geometry (math.DG)Simple (abstract algebra)Mathematics - Quantum AlgebraLie algebraFOS: MathematicssymbolsCovariance and contravariance of vectorsQuantum Algebra (math.QA)Mathematics::Symplectic GeometryMathematical PhysicsJournal of Physics A: Mathematical and General
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