Poisson morphisms and reduced affine Poisson group actions
The symmetry reduction appearing in the study of classical dynamical systems is studied from an abstract point of view. The concept of quotient Poisson group is introduced and some basic properties are established. Then, the reduced Poisson action of the quotient of an affine Poisson group G on the quotient of an affine Poisson G-variety V is studied. It is emphasized that if the quotient Poisson varieties are considered as reduced phase spaces, then the quotient affine Poisson group action may be considered as the symmetry reduction in stages. The Poisson morphisms, including equivalent cases, between Poisson affine varieties are also discussed. It is suggested that the results presented in this paper can be applied to the study of algebraic integrable systems.
scientific article; zbMATH DE number 1885830
scientific article