The Lie bialgebroid of a Poisson-Nijenhuis manifold

DOI10.1007/BF01815524zbMath1005.53060MaRDI QIDQ2563437

Yvette Kosmann-Schwarzbach

Publication date: 4 February 1997

Published in: Letters in Mathematical Physics (Search for Journal in Brave)

zbMATH Keywords

Poisson structureLie bialgebroidLie algebroidNijenhuis structure

Mathematics Subject Classification ID

Poisson manifolds; Poisson groupoids and algebroids (53D17) Poisson algebras (17B63) Pseudogroups and differentiable groupoids (58H05)

Related Items (28)

Dissections and automorphisms of regular Courant algebroids ⋮ Pseudo-Poisson Nijenhuis manifolds ⋮ BIDIFFERENTIAL CALCULI, BICOMPLEX STRUCTURE AND ITS APPLICATION TO BIHAMILTONIAN SYSTEMS ⋮ Vertical and horizontal lifts of multivector fields and applications ⋮ Left-symmetric bialgebroids and their corresponding Manin triples ⋮ Glanon groupoids ⋮ Modular classes of Poisson-Nijenhuis Lie algebroids ⋮ Dirac structures and Nijenhuis operators ⋮ Poisson quasi-Nijenhuis manifolds ⋮ Lie algebroids and Poisson-Nijenhuis structures ⋮ Deformations of symplectic foliations ⋮ Jacobi quasi-Nijenhuis algebroids ⋮ Hom-Poisson-Nijenhuis structures and Hom-Dirac structures ⋮ Vertical lifts of higher order of multivector fields and applications to Poisson geometry ⋮ Poisson quasi-Nijenhuis deformations of the canonical PN structure ⋮ Nambu structures and associated bialgebroids ⋮ A characterization of strict Jacobi-Nijenhuis manifolds through the theory of Lie algebroids ⋮ Variational Poisson-Nijenhuis structures for partial differential equations ⋮ Compatible structures on Lie algebroids and Monge-Ampère operators ⋮ Poisson quasi-Nijenhuis manifolds and the Toda system ⋮ A generalization of Poisson-Nijenhuis structures ⋮ The Euler-Poincaré-Hopf theorem for flat connections in some transitive Lie algebroids ⋮ Integration of holomorphic Lie algebroids ⋮ Poisson-Nijenhuis structures on oriented 3D-manifolds ⋮ Ehresmann doubles and Drinfel'd doubles for Lie algebroids and Lie bialgebroids ⋮ Poisson quasi-Nijenhuis structures with background ⋮ Lie theory of multiplicative tensors ⋮ Local structure of Jacobi--Nijenhuis manifolds

Cites Work

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• The local structure of Poisson manifolds
• Sophus Lie and symplectic geometry
• Lie bialgebroids and Poisson groupoids
• Poisson-Nijenhuis structures and the Vinogradov bracket
• Exact Gerstenhaber algebras and Lie bialgebroids
• The Lie Algebra Structure of Degenerate Hamiltonian and Bi-Hamiltonian Systems

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