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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From homotopy Rota-Baxter algebras to Pre-Calabi-Yau and homotopy double Poisson algebras
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.