Generalizing the notion of Koszul algebra

TL;DR

This paper generalizes Koszul algebras to include graded algebras with relations in various degrees, establishing their fundamental properties and closure under key algebraic operations.

Contribution

It introduces a broad class of generalized Koszul algebras, expanding the classical concept and analyzing their structural properties and examples.

Findings

The class is closed under twists and tensor products.

Includes well-known algebras as special cases.

Provides foundational properties of the generalized class.

Abstract

We introduce a generalization of the notion of a Koszul algebra, which includes graded algebras with relations in different degrees, and we establish some of the basic properties of these algebras. This class is closed under twists, twisted tensor products, regular central extensions and Ore extensions. We explore the monomial algebras in this class and we include some well-known examples of algebras that fall into this class.