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arxiv: math/0506268 · v1 · submitted 2005-06-14 · 🧮 math.QA

A note on noncommutative Poisson structures

William Crawley-Boevey This is my paper
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keywords poissonalgebrasnoncommutativestructuresalgebraassociativeclassifyingdoubled
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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.

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  1. Coupled double Poisson brackets

    math.QA 2026-05 unverdicted novelty 7.0

    Introduces coupled double Poisson brackets, proves bijection to wheeled Poisson brackets, and gives correspondences to Poisson-left-pre-Lie algebras and Yang-Baxter solutions on free polynomial algebras.