Koszul Algebras and Linear Modules: An introduction to the theory of Koszul algebras and linear modules.

Abstract

In this thesis Koszul algebras and their modules, so called linear modules, are introduced. In order to do so, graded $K$-algebras, where $K$ is a field, are also defined and discussed. Furthermore, an isomorphism between split basic finitely $1$-generated graded modules and a path algebra $KGamma/I$ is proved. Linear resolutions are discussed as a preliminary for Koszul algebras. Lastly, the Yoneda algebra $E(Lambda)$ is studied more closely in the case when $Lambda$ is Koszul.