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math.QA2025
Pre-Calabi--Yau algebras and homotopy double Poisson gebras
Johan Leray, Bruno Vallette
We prove that the notion of a curved pre-Calabi--Yau algebra is equivalent to the notion of a curved homotopy double Poisson gebra, thereby settling the equivalence between the two…
math.QA2025
Universal constructions in homotopical algebra
Ricardo Campos, Bruno Vallette
We apply the effective integration theory of Lie-graph algebras, developed recently by the authors, to the deformation and homotopy theories of types of bialgebras, that is structu…
math.QA2025
Integration theory of Lie-graph algebras
Ricardo Campos, Bruno Vallette
We develop the Lie theory of Lie-admissible algebras whose product is enriched with higher operations modeled on directed graphs with a view to apply it to the deformation theories…