Quadratic Poisson structures

DOI10.1063/1.529155zbMath0756.58014OpenAlexW2095103636MaRDI QIDQ3987360

K. Rama, K. H. Bhaskara

Publication date: 28 June 1992

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

Full work available at URL: https://doi.org/10.1063/1.529155

zbMATH Keywords

Poisson structureYang-Baxter equation

Mathematics Subject Classification ID

Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems (37J99) Lie algebras and Lie superalgebras (17B99)

Related Items

Homogeneous Poisson structures, Multi-Hamiltonian structure of the epidemics model accounting for vaccinations and a suitable test for the accuracy of its numerical solvers, Gel'fand-Dorfman theorem and exact cocycle Poisson structures, Poisson structures due to Lie algebra representations, Poisson cohomology of plane quadratic Poisson structures, Becchi–Rouet–Stora–Tyutin structure of polynomial Poisson algebras, On quadratic Poisson structures, Characterization, global analysis and integrability of a family of Poisson structures, New solutions of the Jacobi equations for three-dimensional 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, Separation of variables in the Jacobi identities, New four-dimensional solutions of the Jacobi equations for Poisson structures

Cites Work

• Hamiltonian operators and the classical Yang-Baxter equation
• Solutions of the Yang-Baxter equation
• Some algebraic structures connected with the Yang-Baxter equation
• Some remarks on the transverse Poisson structures of coadjoint orbits
• Discrete groups and the integrability of quantum systems
• Baxter's equations and algebraic geometry
• Yang-Baxter equation and representation theory. I
• Partition function of the eight-vertex lattice model
• ANALOGUES OF THE OBJECTS OF LIE GROUP THEORY FOR NONLINEAR POISSON BRACKETS
• INTRODUCTION TO THE YANG-BAXTER EQUATION
• QUASITRIANGULAR HOPF ALGEBRAS AND YANG-BAXTER EQUATIONS
• Study of Exactly Soluble One-Dimensional N-Body Problems
• Some Exact Results for the Many-Body Problem in one Dimension with Repulsive Delta-Function Interaction