Relation d’équivalence sur les algèbres quasi-Batalin–Vilkovisky différentielles

Differential quasi-Batalin–Vilkovisky algebras are generalisations of differential Batalin–Vilkovisky algebras, introduced by Getzler for applications to topological conformal field theory. As for Lie quasi-bialgebra structures on a finite-dimensional vector space F, we define an equivalence relation on unimodular differential quasi-Batalin–Vilkovisky algebra structures on Λ F∗, the exterior algebra of the dual of F. Therefore, using the relation between Lie quasi-bialgebras and quasi-Batalin–Vilkovisky algebras, we show that unimodular differential quasi-Batalin–Vilkovisky algebra structures on Λ F∗ are equivalent if and only if the corresponding Lie quasi-bialgebra structures on F are equivalent. © 2016, African Mathematical Union and Springer-Verlag Berlin Heidelberg.