0000000000848581

AUTHOR

Pierre-alexandre Gie

showing 2 related works from this author

THE AMITSUR–LEVITZKI THEOREM FOR THE ORTHOSYMPLECTIC LIE SUPERALGEBRA osp(1, 2n)

2006

http://www.worldscinet.com/jaa/05/0503/S0219498806001740.html; International audience; Based on Kostant's cohomological interpretation of the Amitsur–Levitzki theorem, we prove a super version of this theorem for the Lie superalgebras osp(1, 2n). We conjecture that no other classical Lie superalgebra can satisfy an Amitsur–Levitzki type super identity. We show several (super) identities for the standard super polynomials. Finally, a combinatorial conjecture on the standard skew supersymmetric polynomials is stated.

Pure mathematicsAlgebra and Number TheoryConjecture[MATH.MATH-RT]Mathematics [math]/Representation Theory [math.RT]Applied Mathematics010102 general mathematicsMathematics::Rings and AlgebrasSkewLie superalgebraType (model theory)16. Peace & justice01 natural sciences[ MATH.MATH-RT ] Mathematics [math]/Representation Theory [math.RT]Interpretation (model theory)Identity (mathematics)Mathematics::Quantum Algebra0103 physical sciences010307 mathematical physics0101 mathematicsMathematics::Representation TheoryMathematics
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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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