Deformations of Poisson structures by closed 3-forms
Symplectic Geometry
2010-01-06 v1 High Energy Physics - Theory
Mathematical Physics
Differential Geometry
Dynamical Systems
math.MP
Exactly Solvable and Integrable Systems
Abstract
We prove that an arbitrary Poisson structure omega^{ij}(u) and an arbitrary closed 3-form T_{ijk}(u) generate the local Poisson structure A^{ij}(u,u_x) = M^i_s(u,u_x)omega^{sj}(u), where M^i_s(u,u_x)(delta^s_j + omega^{sp}(u)T_{pjk}(u)u^k_x) = delta^i_j, on the corresponding loop space. We obtain also a special graded epsilon-deformation of an arbitrary Poisson structure omega^{ij}(u) by means of an arbitrary closed 3-form T_{ijk}(u).
Keywords
Cite
@article{arxiv.1001.0179,
title = {Deformations of Poisson structures by closed 3-forms},
author = {O. I. Mokhov},
journal= {arXiv preprint arXiv:1001.0179},
year = {2010}
}
Comments
5 pages