Search results for "17B70"

showing 4 items of 4 documents

Metric equivalences of Heintze groups and applications to classifications in low dimension

2021

We approach the quasi-isometric classification questions on Lie groups by considering low dimensional cases and isometries alongside quasi-isometries. First, we present some new results related to quasi-isometries between Heintze groups. Then we will see how these results together with the existing tools related to isometries can be applied to groups of dimension 4 and 5 in particular. Thus we take steps towards determining all the equivalence classes of groups up to isometry and quasi-isometry. We completely solve the classification up to isometry for simply connected solvable groups in dimension 4, and for the subclass of groups of polynomial growth in dimension 5.

Mathematics - Differential GeometrydifferentiaaligeometriaDifferential Geometry (math.DG)Mathematics - Metric GeometryGeneral MathematicsFOS: MathematicsMathematics::Metric GeometryryhmäteoriaMetric Geometry (math.MG)Group Theory (math.GR)20F67 53C23 22E25 17B70 20F69 30L10 54E40Mathematics - Group Theorymetriset avaruudet
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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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Extremal polynomials in stratified groups

2018

We introduce a family of extremal polynomials associated with the prolongation of a stratified nilpotent Lie algebra. These polynomials are related to a new algebraic characterization of abnormal subriemannian geodesics in stratified nilpotent Lie groups. They satisfy a set of remarkable structure relations that are used to integrate the adjoint equations.

Statistics and Probabilityextremal polynomialsMathematics - Differential GeometryPure mathematicsGeodesicStructure (category theory)Group Theory (math.GR)Characterization (mathematics)algebra01 natural sciencesdifferentiaaligeometriaMathematics - Analysis of PDEsMathematics - Metric Geometry53C17FOS: Mathematics0101 mathematicsAlgebraic numberMathematics - Differential Geometry; Mathematics - Differential Geometry; Mathematics - Analysis of PDEs; Mathematics - Group Theory; Mathematics - Metric Geometry; Mathematics - Optimization and Control; 53C17; 49K30; 17B70Mathematics - Optimization and ControlMathematics010102 general mathematicsStatisticsta111polynomitProlongation53C17 49K30 17B70Lie groupMetric Geometry (math.MG)abnormal extremals010101 applied mathematicsNilpotent Lie algebraNilpotentsub-Riemannian geometryabnormal extremals extremal polynomials Carnot groups sub-Riemannian geometryAbnormal extremals; Carnot groups; Extremal polynomials; Sub-Riemannian geometry; Analysis; Statistics and Probability; Geometry and Topology; Statistics Probability and UncertaintyDifferential Geometry (math.DG)Optimization and Control (math.OC)Carnot groups17B70Probability and UncertaintyGeometry and TopologyStatistics Probability and UncertaintyMathematics - Group TheoryAnalysisAnalysis of PDEs (math.AP)Mathematics - Differential Geometry; Mathematics - Differential Geometry; Mathematics - Analysis of PDEs; Mathematics - Group Theory; Mathematics - Metric Geometry; Mathematics - Optimization and Control; 53C17 49K30 17B7049K30
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New applications of graded Lie algebras to Lie algebras, generalized Lie algebras and cohomology

2007

We give new applications of graded Lie algebras to: identities of standard polynomials, deformation theory of quadratic Lie algebras, cyclic cohomology of quadratic Lie algebras, $2k$-Lie algebras, generalized Poisson brackets and so on.

[MATH.MATH-RT]Mathematics [math]/Representation Theory [math.RT]2k-Lie algebrasstandard polynomial.standard polynomial[ MATH.MATH-RT ] Mathematics [math]/Representation Theory [math.RT]Deformation theoryGerstenhaber-Nijenhuis bracketFOS: Mathematicsgraded Lie algebrasquadratic Lie algebra[MATH.MATH-RT] Mathematics [math]/Representation Theory [math.RT]Representation Theory (math.RT)Gerstenhaber bracketcyclic cohomologysuper Poisson bracketsMathematics - Representation TheorySchouten bracket17B70 17B05 17B20 17B56 17B60 17B65
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