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.
A note on noncommutative Poisson structures
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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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2026 2verdicts
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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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Double Transposed Poisson Algebras
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.