Differential Projective Modules Over Algebras with Radical Square Zero

Abstract

Let Q be a finite connected quiver and Λ be the radical square zero algebra of Q. We give a bijection between the reduced differential projective modules over Λ and the representations of the opposite quiver of Q. If Q has oriented cycles and Q is not a basic cycle, we prove that the algebra of dual numbers over Λ is not virtually Gorenstein.