Weinstein, Alan 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 Keywords:Poisson structures; Symplectic leaves; Casimir functions; Transverse structures; coadjoint orbits; Reduction; dual pairs; Integrable systems; Stability Citations:Zbl 0573.00010; Zbl 0524.58011 PDFBibTeX XML