Co-Point Modules Over Frobenius Koszul Algebras

Abstract

Let A be a Frobenius Koszul algebra such that its Koszul dual A ! is a quantum polynomial algebra. Co-point modules over A were defined as dual notion of point modules over A ! with respect to the Koszul duality. In this article, we will see that various important functors between module categories over A used in representation theory of finite dimensional algebras send co-point modules to co-point modules. As a consequence, we will show that if (E, σ) is a geometric pair associated to A !, then the map σ:E → E is an automorphism of the point scheme E of A !, so that there is a bijection between isomorphism classes of left point modules over A ! and those of right point modules over A !.