A note on noncommutative Poisson structures

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

References in corpus (1)

• Noncommutative Geometry and Quiver algebras

Cited by in corpus (5)

• On the noncommutative Poisson geometry of certain wild character varieties
• The global extension problem, crossed products and co-flag non-commutative Poisson algebras
• Nonabelian elliptic Poisson structures on projective spaces
• Euler continuants in noncommutative quasi-Poisson geometry
• Pre-Calabi-Yau algebras and noncommutative calculus on higher cyclic Hochschild cohomology