A note on noncommutative Poisson structures
arXiv:math/0506268
Abstract
We introduce a new type of noncommutative Poisson structure on associative algebras. It induces Poisson structures on the moduli spaces classifying semisimple modules. Path algebras of doubled quivers and preprojective algebras have noncommutative Poisson structures given by the necklace Lie algebra.
6 pages