Exact Results in Quantum Theory

In a recent paper Vladimir Sokolov introduces a three-parametric family of quadratic Poisson structures on gl(3) each of which is compatible with the canonical linear Poisson bracket. The complete involutive family of polynomial functions related to these bi-Poisson structures contains the Hamiltonian of the so-called elliptic Calogero-Moser system, the quantum version of which is also discussed in the same paper.We show that there exists a 10-parametric family of quadratic Poisson structures on gl(3) compatible with the canonical linear Poisson bracket and containing the Sokolov family. The quantization matters will be also touched in this talk. (The joint work with Ihor Mykytyuk.)