Search results for " 17B30"

showing 2 items of 2 documents

Singular quadratic Lie superalgebras

2012

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.

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 representation
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The action of a compact Lie group on nilpotent Lie algebras of type {{n,2}}

2015

Abstract We classify finite-dimensional real nilpotent Lie algebras with 2-dimensional central commutator ideals admitting a Lie group of automorphisms isomorphic to SO 2 ⁢ ( ℝ ) ${{\mathrm{SO}}_{2}(\mathbb{R})}$ . This is the first step to extend the class of nilpotent Lie algebras 𝔥 ${{\mathfrak{h}}}$ of type { n , 2 } ${\{n,2\}}$ to solvable Lie algebras in which 𝔥 ${{\mathfrak{h}}}$ has codimension one.

pair of alternating formsPure mathematicsClass (set theory)General MathematicsGroup Theory (math.GR)010103 numerical & computational mathematicsType (model theory)01 natural sciencesMathematics::Group TheoryTermészettudományokLie algebraFOS: MathematicsMatematika- és számítástudományok0101 mathematicsNilpotent Lie algebraMathematicsCommutatorApplied Mathematics010102 general mathematicsLie groupCodimensionAutomorphismNilpotent17B05 17B30 15A63&nbspSettore MAT/03 - GeometriaMathematics - Group TheoryForum Mathematicum
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