A generalized Koszul theory and its relation to the classical theory

Abstract

Let $A={⨁}_{i⩾0}{A}_i$ be a graded locally finite $k$-algebra such that $A_0$ is an arbitrary finite-dimensional algebra satisfying a certain splitting condition. In this paper we develop a generalized Koszul theory preserving many classical results. Moreover, we define a quotient graded algebra $\bar{A}={⨁}_{i⩾0}{\bar{A}}_i$ and show that $A$ is a generalized Koszul algebra if and only if $\bar{A}$ is a classical Koszul algebra and a projective $A_0$-module. We also describe an application of this theory to the extension algebras of standard modules of standardly stratified algebras.

Correct a serious mistake of the crucial Lemma 3.4 and Theorem 3.6

References in corpus (1)

• First extension groups of Verma modules and $R$-polynomials