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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