The affine group as symplectic manifold

DOI10.2748/tmj/1178225893zbMath0784.53031OpenAlexW2070146218MaRDI QIDQ1313230

Alberto Medina, Ali Quadfel, Martin Bordemann

Publication date: 26 January 1994

Published in: Tôhoku Mathematical Journal. Second Series (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.2748/tmj/1178225893

zbMATH Keywords

affine groupHamiltonian actionLagrangian foliationsymplectic Lie groupsymplectic embedding

Mathematics Subject Classification ID

Differential geometry of homogeneous manifolds (53C30) General geometric structures on manifolds (almost complex, almost product structures, etc.) (53C15)

Related Items (15)

Flat affine or projective geometries on Lie groups ⋮ Symmetry analysis, integrability and completeness of geodesics of a double of the affine Lie group of the real line ⋮ Structure of symplectic Lie groups and momentum map ⋮ Flat symplectic Lie algebras ⋮ Unnamed Item ⋮ Invariant structures on Lie groups ⋮ Uniqueness of left invariant symplectic structures on the affine Lie group ⋮ Bi-Lagrangian structure on the symplectic affine Lie algebra of \(\mathbb{R}^2\) ⋮ Left invariant Poisson structures on classical non-compact simple Lie groups ⋮ Left invariant contact structures on Lie groups ⋮ Solutions of the classical Yang-Baxter equation and noncommutative deformations ⋮ Some non-abelian phase spaces in low dimensions ⋮ Symplectic structures on the filiform Lie algebras ⋮ Complex, symplectic, and contact structures on low-dimensional Lie groups ⋮ Coeffective and de Rham cohomologies of symplectic manifolds

Cites Work

• Generalized Lax pairs, the modified classical Yang-Baxter equation, and affine geometry of Lie groups
• On Lie groups with left-invariant symplectic or Kählerian structures
• Poisson Lie groups, dressing transformations, and Bruhat decompositions
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