×

zbMATH — the first resource for mathematics

Poisson structures and Lie algebras. (English) Zbl 0608.58027
Élie Cartan et les mathématiques d’aujourd’hui, The mathematical heritage of Elie Cartan, Semin. Lyon 1984, Astérisque, No.Hors Sér. 1985, 421-434 (1985).
[For the entire collection see Zbl 0573.00010.]
The paper is a survey report on the developments of the theory of Poisson structures, a theory which is mainly due to the author himself [J. Differ. Geom. 18, 523-557 (1983; Zbl 0524.58011)]. This report has the following sections: Definitions and first properties, Symplectic leaves and Casimir functions, Linearization, Transverse structures to coadjoint orbits, Reduction and dual pairs, Integrable systems, Stability. It also contains an extensive bibliography.
Reviewer: I.Vaisman

MSC:
37J99 Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems
37C85 Dynamics induced by group actions other than \(\mathbb{Z}\) and \(\mathbb{R}\), and \(\mathbb{C}\)
17B99 Lie algebras and Lie superalgebras