Poisson homology of r-matrix type orbits I: example of computation
Differential Geometry
2015-06-26 v2 Quantum Algebra
Exactly Solvable and Integrable Systems
Abstract
In this paper we consider the Poisson algebraic structure associated with a classical -matrix, i.e. with a solution of the modified classical Yang--Baxter equation. In Section 1 we recall the concept and basic facts of the -matrix type Poisson orbits. Then we describe the -matrix Poisson pencil (i.e the pair of compatible Poisson structures) of rank 1 or -type orbits of . Here we calculate symplectic leaves and the integrable foliation associated with the pencil. We also describe the algebra of functions on -type orbits. In Section 2 we calculate the Poisson homology of Drinfeld--Sklyanin Poisson brackets which belong to the -matrix Poisson family.
Keywords
Cite
@article{arxiv.math/9812146,
title = {Poisson homology of r-matrix type orbits I: example of computation},
author = {Alexei Kotov},
journal= {arXiv preprint arXiv:math/9812146},
year = {2015}
}