Generalized Lie bialgebras and Jacobi structures on Lie groups.

DOI10.1007/BF02773071zbMath1059.17014arXivmath/0102171OpenAlexW2031598723WikidataQ115391657 ScholiaQ115391657MaRDI QIDQ1870919

David Iglesias, Juan Carlos Marrero

Publication date: 9 July 2003

Published in: Israel Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0102171

zbMATH Keywords

Lie bialgebroidscontact formsJacobi structuresmultiplicative tensors

Mathematics Subject Classification ID

Poisson manifolds; Poisson groupoids and algebroids (53D17) Lie algebras of Lie groups (22E60) Contact manifolds (general theory) (53D10) Lie bialgebras; Lie coalgebras (17B62)

Related Items

Jacobi-Lie Hamiltonian Systems on Real Low-Dimensional Jacobi-Lie Groups and their Lie Symmetries, Classification of real low-dimensional Jacobi (generalized)–Lie bialgebras, Jacobi-Lie symmetry and Jacobi-Lie T-dual sigma models on group manifolds, Riemannian geometry on contact Lie groups, On locally conformal symplectic manifolds of the first kind, Jacobi groupoids and generalized Lie bialgebroids., Infinitesimal Automorphisms of VB-Groupoids and Algebroids, Left invariant contact structures on Lie groups, Generalized Lie bialgebroids and Jacobi structures, Classical r-matrices of real low-dimensional Jacobi–Lie bialgebras and their Jacobi–Lie groups

Cites Work

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• The local structure of Poisson manifolds
• On contact manifolds
• Géométrie des algèbres de Lie locales de Kirillov
• Locally conformal symplectic manifolds
• Symplectic reduction, BRS cohomology, and infinite-dimensional Clifford algebras
• Structure locale des variétés de Jacobi. (Local structure of Jacobi manifolds)
• On Lie groups with left-invariant symplectic or Kählerian structures
• Poisson Lie groups, dressing transformations, and Bruhat decompositions
• Matched pairs of Lie groups associated to solutions of the Yang-Baxter equations
• Les variétés de Poisson et leurs algèbres de Lie associees
• Les variétés de Jacobi et leurs algèbres de Lie associees
• Lectures on the geometry of Poisson manifolds
• Lie bialgebroids and Poisson groupoids
• Exact Gerstenhaber algebras and Lie bialgebroids
• Symplectic double extension of a symplectic Lie group
• Sur l'espace de prolongement différentiable
• The Lie Algebra Structure of Degenerate Hamiltonian and Bi-Hamiltonian Systems
• Jacobi structures revisited
• Generalized lie bialgebras
• LOCAL LIE ALGEBRAS
• Some linear Jacobi structures on vector bundles
• The BV-algebra of a Jacobi manifold
• Symplectic Homogeneous Spaces
• Generalized Lie bialgebroids and Jacobi structures