Search results for "Super Poisson bracket"

showing 2 items of 2 documents

Singular quadratic Lie superalgebras

2012

In this paper, we give a generalization of results in \cite{PU07} and \cite{DPU10} by applying the tools of graded Lie algebras to quadratic Lie superalgebras. In this way, we obtain a numerical invariant of quadratic Lie superalgebras and a classification of singular quadratic Lie superalgebras, i.e. those with a nonzero invariant. Finally, we study a class of quadratic Lie superalgebras obtained by the method of generalized double extensions.

Pure mathematics17B05Super Poisson bracketFOS: Physical sciencesLie superalgebraGraded Lie algebraRepresentation of a Lie groupMathematics::Quantum AlgebraMathematics::Representation TheoryMathematical PhysicsMathematicsQuadratic Lie superalgebrasDiscrete mathematicsAlgebra and Number TheoryInvariant[MATH.MATH-RT]Mathematics [math]/Representation Theory [math.RT]Simple Lie groupMathematics::Rings and AlgebrasMathematical Physics (math-ph)17B30Killing form[ MATH.MATH-RT ] Mathematics [math]/Representation Theory [math.RT]Lie conformal algebraDouble extensionsGeneralized double extensionsAdjoint representation of a Lie algebra15A63 17B05 17B30 17B70Adjoint orbits 2000 MSC: 15A6317B70Fundamental representation
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New applications of graded Lie algebras to Lie algebras, generalized Lie algebras and cohomology

2007

We give new applications of graded Lie algebras to: identities of standard polynomials, deformation theory of quadratic Lie algebras, cyclic cohomology of quadratic Lie algebras, $2k$-Lie algebras, generalized Poisson brackets and so on.

[MATH.MATH-RT]Mathematics [math]/Representation Theory [math.RT]2k-Lie algebrasstandard polynomial.standard polynomial[ MATH.MATH-RT ] Mathematics [math]/Representation Theory [math.RT]Deformation theoryGerstenhaber-Nijenhuis bracketFOS: Mathematicsgraded Lie algebrasquadratic Lie algebra[MATH.MATH-RT] Mathematics [math]/Representation Theory [math.RT]Representation Theory (math.RT)Gerstenhaber bracketcyclic cohomologysuper Poisson bracketsMathematics - Representation TheorySchouten bracket17B70 17B05 17B20 17B56 17B60 17B65
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