5 papers
Operadic Calculus for Higher Colour-Kinematics Duality
Anibal M. Medina-Mardones, Bruno Vallette
The search for algebraic foundations of colour-kinematics duality and the double-copy construction has brought into focus a generalization of Batalin--Vilkovisky algebras, referred…
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…
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…
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…
Simplicial properadic homotopy
Eric Hoffbeck, Johan Leray, Bruno Vallette
In this paper, we settle the homotopy properties of the infinity-morphisms of homotopy (bial)-gebras over properads, i.e. algebraic structures made up of operations with several in…