Search results for "Jordan algebras"

showing 2 items of 2 documents

Ordinary and graded cocharacter of the Jordan algebra of 2x2 upper triangular matrices

2014

Abstract Let F be a field of characteristic zero and U J 2 ( F ) be the Jordan algebra of 2 × 2 upper triangular matrices over F . In this paper we give a complete description of the space of multilinear graded and ordinary identities in the language of Young diagrams through the representation theory of a Young subgroup of S n . For every Z 2 -grading of U J 2 ( F ) we compute the multiplicities in the graded cocharacter sequence and furthermore we compute the ordinary cocharacter.

Discrete mathematicsNumerical AnalysisSequenceMultilinear mapPure mathematicsAlgebra and Number TheoryJordan algebraZero (complex analysis)Triangular matrixField (mathematics)Space (mathematics)Representation theoryJordan algebras Polynomial identities Basis of identities Cocharacter Gradings Graded polynomial identitiesSettore MAT/02 - AlgebraDiscrete Mathematics and CombinatoricsGeometry and TopologyMathematics
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Un nouvel invariant des algèbres de Lie et des super-algèbres de Lie quadratiques

2011

In this thesis, we defind a new invariant of quadratic Lie algebras and quadratic Lie superalgebras and give a complete study and classification of singular quadratic Lie algebras and singular quadratic Lie superalgebras, i.e. those for which the invariant does not vanish. The classification is related to adjoint orbits of Lie algebras o(m) and sp(2n). Also, we give an isomorphic characterization of 2-step nilpotent quadratic Lie algebras and quasi-singular quadratic Lie superalgebras for the purpose of completeness. We study pseudo-Euclidean Jordan algebras obtained as double extensions of a quadratic vector space by a one-dimensional algebra and 2-step nilpotent pseudo-Euclidean Jordan al…

Generalized double extensionInvariantPseudo-Eucliean Jordan algebras[ MATH.MATH-GM ] Mathematics [math]/General Mathematics [math.GM]Lie algebra sp(2n)Pas de mot clé en français[MATH.MATH-GM] Mathematics [math]/General Mathematics [math.GM]Symmetric Novikov algebrasSolvable Lie algebrasDouble extensionsQuadratic Lie algebras[MATH.MATH-GM]Mathematics [math]/General Mathematics [math.GM]Adjoint orbitsT*-extension2-step nilpotentJordan-admissibleQuadratic Lie superalgebrasLie algebra o(m)
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