Cohomology Structures of A Poisson Algebra: II
Representation Theory
2019-12-03 v2 Quantum Algebra
Abstract
We introduce for any Poisson algebra a bicomplex of free Poisson modules, and use it to show that the Poisson cohomology theory introduced in the paper "[M. Flato, M. Gerstenhaber and A. A. Voronov, Cohomology and Deformation of Leibniz Pairs, Lett. Math. Phys. 34 (1995) 77--90]" is given by certain derived functor. Moreover, by constructing a long exact sequence connecting Poisson cohomology groups and Yoneda-extension groups of certain quasi-Poisson modules, we provide a way to compute this Poisson cohomology via the Lie algebra cohomology and the Hochschild cohomology.
Keywords
Cite
@article{arxiv.1212.3756,
title = {Cohomology Structures of A Poisson Algebra: II},
author = {Yan-Hong Bao and Yu Ye},
journal= {arXiv preprint arXiv:1212.3756},
year = {2019}
}
Comments
18pages