6533b839fe1ef96bd12a5b37
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Back to the Amitsur-Levitzki theorem: a super version for the orthosymplectic Lie superalgebra osp(1, 2n)
Rosane UshirobiraPierre-alexandre GieGeorges Pinczonsubject
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 Theorydescription
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).
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2003-09-25 |