Nijenhuis geometry. II: Left-symmetric algebras and linearization problem for Nijenhuis operators

DOI10.1016/j.difgeo.2020.101706zbMath1477.17105arXiv1903.06411OpenAlexW3113121056WikidataQ115354662 ScholiaQ115354662MaRDI QIDQ1995666

Andrey Yu. Konyaev

Publication date: 24 February 2021

Published in: Differential Geometry and its Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1903.06411

zbMATH Keywords

left-symmetric algebraNijenhuis operatorlinearisation problem

Mathematics Subject Classification ID

Local differential geometry (53B99) Lie-admissible algebras (17D25)

Related Items (15)

On the linearization of certain singularities of Nijenhuis operators ⋮ Nijenhuis geometry. III: \(\mathrm{gl}\)-regular Nijenhuis operators ⋮ Applications of Nijenhuis geometry. V: Geodesic equivalence and finite-dimensional reductions of integrable quasilinear systems ⋮ Nijenhuis operators and associative D-bialgebras ⋮ Symmetric matrices and maximal Nijenhuis pencils;Симметрические матрицы и максимальные нийенхейсовы пучки ⋮ Elementary differential singularities of three-dimensional Nijenhuis operators ⋮ Integrating Nijenhuis structures ⋮ Applications of Nijenhuis geometry. III: Frobenius pencils and compatible non-homogeneous Poisson structures ⋮ Almost differentially nondegenerate Nijenhuis operators ⋮ Nijenhuis geometry ⋮ The classification of left-invariant para-Kähler structures on simply connected four-dimensional Lie groups ⋮ Applications of Nijenhuis geometry II: maximal pencils of multi-Hamiltonian structures of hydrodynamic type ⋮ Singularities of two-dimensional Nijenhuis operators ⋮ Applications of Nijenhuis geometry: non-degenerate singular points of Poisson-Nijenhuis structures ⋮ On k-para-Kähler Lie algebras, a subclass of k-symplectic Lie algebras

Cites Work

• The local structure of Poisson manifolds
• Complex analytic coordinates in almost complex manifolds
• Simple left-symmetric algebras with solvable Lie algebra
• Compatible flat metrics
• Geometrical interpretation of Benenti systems
• Nijenhuis geometry
• Left-symmetric algebras, or pre-Lie algebras in geometry and physics
• Linearization of resonant vector fields
• Equivalence and Decomposition of Vector Fields About an Elementary Critical Point
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