Search results for "Nilpotent lie algebra"

showing 2 items of 12 documents

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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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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