On classification of discrete, scalar-valued Poisson brackets
This paper gives a classification of discrete and scalar-valued Poisson brackets. Let us recall that he Poisson brackets were introduced by Drubovin as a dicretization of the differential geometric Poisson brackets. In this work, the author describes a procedure to classify discrete differential-geometric Poisson brackets of any order on a target space of dimension 1. Then, using a change of coordinates, he proves that any scalar-valued Poisson bracket can be reduced to the cubic Poisson bracket of a Volterra lattice. Finally, the notion of admissible Lie-Poisson groups is introduced and a procedure to produce new classes of non degenerate vector-valued first order differential geometric Poisson brackets is described.
scientific article; zbMATH DE number 6069294
scientific article