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.
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The dioperad Y^{(n)} is Koszul, shown by analyzing subcomplexes of assocoipahedra via their correspondence to cloven Strebel differentials on CP^1 and deducing vanishing higher cohomology.
The paper shows that cyclic homotopy Rota-Baxter structures on interactive pairs of dg-algebras induce pre-Calabi-Yau and homotopy double Poisson structures on the base algebra, including homotopy double Lie structures on modules.
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Coupled double Poisson brackets
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.