Resolutions over Koszul algebras

Abstract.In this paper we show that if $$\Lambda = \mathop \coprod \limits_{i \geqq 0} \Lambda _i $$ is a Koszul algebra with Λ0 isomorphic to a product of copies of a field, then the minimal projective resolution of Λ0 as a right Λ-module provides all the information necessary to construct both a minimal projective resolution of Λ0 as a left Λ-module and a minimal projective resolution of Λ as a right module over the enveloping algebra of Λ. The main tool for this is showing that there is a comultiplicative structure on a minimal projective resolution of Λ0 as a right Λ-module.