Normal forms of Poisson structures in three-dimensional space. (English. Russian original) Zbl 0877.58023

Lychagina, O. V.

Russ. Math. Surv. 51, No. 4, 741-742 (1996); translation from Usp. Mat. Nauk 51, No. 4, 163-164 (1996).

The paper provides a formal classification of degenerate Poisson structures in three-dimensional space \(\mathbb{R}^3\). The proofs are based on the calculation of the spectral sequence constructed in the author’s preprint [‘Schouten brackets and Lie-Sklyanin algebras’, Preprint ISBN 82-553-0962-4, No. 18, Univ. Oslo: Inst. Math., 1-28 (1995)].

Reviewer: G.Osipenko (St.Peterburg)

MSC:

37J99	Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems
37G05	Normal forms for dynamical systems

Keywords:

degenerate Poisson structure; Lie algebra; cubic polynomial; normal forms