GRADED MORITA EQUIVALENCES FOR FROBENIUS KOSZUL ALGEBRAS AND SYMMETRIC ALGEBRAS (Cohomology theory of finite groups and related topics)

Abstract

Let k be an algebraically closed field of characteristic 0 and Λ a finite-dimensional k-algebra. In this report, we show that, for a Frobenius Koszul algebra A with (rad Λ)4 = 0, there exists a symmetric Koszul algebra S such that Λ and S are graded Morita equivalent. This result tells us a new difference between the category of modules over non-graded algebras and the category of modules over graded algebras. This proof is given by the methods of non-commutative algebraic geometry throughout a Koszul duality.