Triangular matrix and Koszul algebras

Abstract

It is well known that Koszul algebras are quadratic and monomial quadratic algebras [7] and quadratic algebras of global dimension two are Koszul. It was also proved in [4] that algebras with a quadratic Groebner basis are Koszul, however there is no general characterization of Koszul algebras, hence it is of interest to construct new Koszul algebras from given ones. The aim of the paper is to find sufficent conditions on K-algebras R and T and a T -R bimodule M in order to have