A classification of algebras stratified for all preorders by Koszul theory

TL;DR

This paper develops a generalized Koszul theory to classify all algebras stratified for any preorder, extending classical results to a broader algebraic context.

Contribution

It introduces a unified framework for Koszul theory applicable to a wide class of stratified algebras based on arbitrary preorders.

Findings

Generalized Koszul theory applicable to various algebra classes

Classification of algebras stratified for all preorders

Extension of classical Koszul results

Abstract

Let $A = \bigoplus_{i \geqslant 0} A_i$ be a graded locally finite $k$-algebra such that $A_0$ is an arbitrary finite-dimensional algebra satisfying some splitting condition. In this paper we develop a generalized Koszul theory generalizing many classical results, and use it to classify algebras stratified for all preorders.