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A note on noncommutative Poisson structures

· 2005 · math.QA · arXiv math/0506268

2 Pith papers cite this work. Polarity classification is still indexing.

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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.

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math.QA 1 math.RT 1

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2026 2

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UNVERDICTED 2

representative citing papers

Coupled double Poisson brackets

math.QA · 2026-05-17 · 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.

Double Transposed Poisson Algebras

math.RT · 2026-07-01 · unverdicted · novelty 6.0

Double transposed Poisson algebras on unital associative algebras are governed by a single derivation to A tensor S(A over commutators), inducing GL_N-equivariant transposed Poisson structures on representation algebras and their invariants via trace maps.

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Showing 2 of 2 citing papers.

  • Coupled double Poisson brackets math.QA · 2026-05-17 · unverdicted · none · ref 83 · internal anchor

    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.

  • Double Transposed Poisson Algebras math.RT · 2026-07-01 · unverdicted · none · ref 3 · internal anchor

    Double transposed Poisson algebras on unital associative algebras are governed by a single derivation to A tensor S(A over commutators), inducing GL_N-equivariant transposed Poisson structures on representation algebras and their invariants via trace maps.