On quadratic Poisson structures

DOI10.1007/BF00420516zbMath0773.58007OpenAlexW2022449575MaRDI QIDQ1202950

Ping Xu, Zhang-Ju Liu

Publication date: 20 April 1993

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

Full work available at URL: https://doi.org/10.1007/bf00420516

zbMATH Keywords

classification problemsclassical \(r\)-matrixquadratic Poisson structure

Mathematics Subject Classification ID

Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems (37J99)

Related Items (37)

Homogeneous Poisson structures ⋮ New solution family of the Jacobi equations: Characterization, invariants, and global Darboux analysis ⋮ Multi-Hamiltonian structure of the epidemics model accounting for vaccinations and a suitable test for the accuracy of its numerical solvers ⋮ Poisson cohomology of plane quadratic Poisson structures ⋮ The modular automorphism group of a Poisson manifold ⋮ Compatible Poisson structures on fibered 5-manifolds ⋮ Poisson geometry ⋮ Quadratic Poisson algebras and their infinite-dimensional extensions ⋮ SKLYANIN BRACKET AND DEFORMATION OF THE CALOGERO–MOSER SYSTEM ⋮ Quadratic deformations of Lie-Poisson structures ⋮ Uniqueness of left invariant symplectic structures on the affine Lie group ⋮ Generalization of solutions of the Jacobi PDEs associated to time reparametrizations of Poisson systems ⋮ Poisson cohomology of plane Poisson structures with isolated singularities revisited ⋮ Left invariant Poisson structures on classical non-compact simple Lie groups ⋮ On computational Poisson geometry. II. Numerical methods ⋮ Linear Poisson structures on \(\mathbb R^4\) ⋮ The modular hierarchy of the Toda lattice ⋮ On toric Poisson structures of type \((1,1)\) and their cohomology ⋮ Integrable hierarchies and the modular class ⋮ Characterization, global analysis and integrability of a family of Poisson structures ⋮ New solutions of the Jacobi equations for three-dimensional Poisson structures ⋮ On one class of exact Poisson structures ⋮ Characterization and global analysis of a family of Poisson structures ⋮ One solution of the 3D Jacobi identities allows determining an infinity of them ⋮ Unimodularity and preservation of volumes in nonholonomic mechanics ⋮ COHOMOLOGIE DE CERTAINS BI-COMPLEXES ET APPLICATIONS AUX STRUCTURES DE POISSON ⋮ On the integrability of deformation quantized Toda lattice ⋮ Separation of variables in the Jacobi identities ⋮ Poisson-Nijenhuis structures on oriented 3D-manifolds ⋮ Poisson structures and generalized Kähler submanifolds ⋮ On computational Poisson geometry. I: Symbolic foundations ⋮ Differential forms on vector bundles ⋮ Quantization of quadratic Poisson brackets on a polynomial algebra of three variables ⋮ Normal forms of Poisson structures with zero 1-jet at a point ⋮ Relative modular classes of Lie algebroids ⋮ New four-dimensional solutions of the Jacobi equations for Poisson structures ⋮ Quantum deformations of projective three-space

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Poisson geometry of the principal series and nonlinearizable structures
• Morita equivalence of Poisson manifolds
• Deformation quantization of Heisenberg manifolds
• ANALOGUES OF THE OBJECTS OF LIE GROUP THEORY FOR NONLINEAR POISSON BRACKETS
• Quadratic Poisson structures
• Morita equivalence and symplectic realizations of Poisson manifolds
• Symplectic groupoids and Poisson manifolds

This page was built for publication: On quadratic Poisson structures