6533b871fe1ef96bd12d174d
RESEARCH PRODUCT
Un nouvel invariant des algèbres de Lie et des super-algèbres de Lie quadratiques
Minh Thanh Duongsubject
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)description
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 algebras, in the same manner as it was done for singular quadratic Lie algebras and 2-step nilpotent quadratic Lie algebras. Finally, we focus on the case of a symmetric Novikov algebra and study it up to dimension 7.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2011-07-06 |