Equivalence of Chiral Algebras with Abelian Conformal Structure to Differential Algebras
This paper establishes an equivalence between chiral algebras with an abelian conformal structure and differential algebras. Specifically, it demonstrates that the variety of chiral algebras defined by a binary quadratic operad Var with an abelian conformal part is identical to the variety of differential algebras defined by the Manin product of Var and the operad of associative commutative algebras (Com). This result is achieved through a categorical approach.