Uniqueness of left invariant symplectic structures on the affine Lie group

DOI10.1090/S0002-9939-01-05828-2zbMath1021.53052OpenAlexW1557273726WikidataQ115290193 ScholiaQ115290193MaRDI QIDQ2716119

Yoshio Agaoka

Publication date: 6 June 2001

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s0002-9939-01-05828-2

zbMATH Keywords

Poisson structurePfaffianclassical Yang-Baxter equationaffine Lie groupleft invariant symplectic structure

Mathematics Subject Classification ID

Differential geometry of homogeneous manifolds (53C30) Symplectic manifolds (general theory) (53D05) Poisson manifolds; Poisson groupoids and algebroids (53D17) Poisson algebras (17B63)

Related Items (6)

An algorithm to determine the isomorphism classes of 4-dimensional complex Lie algebras ⋮ Symmetry analysis, integrability and completeness of geodesics of a double of the affine Lie group of the real line ⋮ Eight-dimensional symplectic non-solvable Lie algebras ⋮ Bi-Lagrangian structure on the symplectic affine Lie algebra of \(\mathbb{R}^2\) ⋮ Left invariant Poisson structures on classical non-compact simple Lie groups ⋮ Unnamed Item

Cites Work

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• On quadratic Poisson structures
• On Lie algebras having a primitive universal enveloping algebra
• The affine group as symplectic manifold
• Lectures on the geometry of Poisson manifolds
• Symplectic double extension of a symplectic Lie group
• Left invariant Poisson structures on classical non-compact simple Lie groups
• The maximal subgroups of the classical groups
• Constant solutions of Yang-Baxter equation for $\mathfrak{sl}(2)$ and $\mathfrak{sl}(3)$.
• On frobenius lie algebras
• A classification of irreducible prehomogeneous vector spaces and their relative invariants

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