Search results for "17B20"

showing 2 items of 2 documents

Back to the Amitsur-Levitzki theorem: a super version for the orthosymplectic Lie superalgebra osp(1, 2n)

2003

We prove an Amitsur-Levitzki type theorem for the Lie superalgebras osp(1,2n) inspired by Kostant's cohomological interpretation of the classical theorem. We show that the Lie superalgebras gl(p,q) cannot satisfy an Amitsur-Levitzki type super identity if p, q are non zero and conjecture that neither can any other classical simple Lie superalgebra with the exception of osp(1,2n).

Lie superalgebraType (model theory)17B2001 natural sciencesInterpretation (model theory)CombinatoricsIdentity (mathematics)Simple (abstract algebra)Mathematics::Quantum Algebra0103 physical sciencesFOS: Mathematics0101 mathematicsRepresentation Theory (math.RT)Classical theoremMathematics::Representation TheoryMathematical PhysicsPhysicsConjecture[MATH.MATH-RT]Mathematics [math]/Representation Theory [math.RT]010308 nuclear & particles physics010102 general mathematicsMathematics::Rings and AlgebrasStatistical and Nonlinear Physics16. Peace & justice17B56[ MATH.MATH-RT ] Mathematics [math]/Representation Theory [math.RT]17B20; 17B56Mathematics - Representation Theory
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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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