6533b86cfe1ef96bd12c8d73
RESEARCH PRODUCT
Singular quadratic Lie superalgebras
Rosane UshirobiraRosane UshirobiraMinh Thanh Duongsubject
Pure mathematics17B05Super Poisson bracketFOS: Physical sciencesLie superalgebraGraded Lie algebraRepresentation of a Lie groupMathematics::Quantum AlgebraMathematics::Representation TheoryMathematical PhysicsMathematicsQuadratic Lie superalgebrasDiscrete mathematicsAlgebra and Number TheoryInvariant[MATH.MATH-RT]Mathematics [math]/Representation Theory [math.RT]Simple Lie groupMathematics::Rings and AlgebrasMathematical Physics (math-ph)17B30Killing form[ MATH.MATH-RT ] Mathematics [math]/Representation Theory [math.RT]Lie conformal algebraDouble extensionsGeneralized double extensionsAdjoint representation of a Lie algebra15A63 17B05 17B30 17B70Adjoint orbits 2000 MSC: 15A6317B70Fundamental representationdescription
In this paper, we give a generalization of results in \cite{PU07} and \cite{DPU10} by applying the tools of graded Lie algebras to quadratic Lie superalgebras. In this way, we obtain a numerical invariant of quadratic Lie superalgebras and a classification of singular quadratic Lie superalgebras, i.e. those with a nonzero invariant. Finally, we study a class of quadratic Lie superalgebras obtained by the method of generalized double extensions.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2012-06-24 |