Graded quotients of path algebras: A local theory
The paper is a discussion of quotient algebras of path algebras of quivers on which groups act. By defining some subcategories of the categories of graded modules for a subset of the given group and the consideration of the relation between them, a local theory of graded modules is introduced. In this way, the authors show that if a graded ring is a quotient of a path algebra with a partial group action then one may retrieve the original algebra from knowledge of the local theory. Also, almost split sequences for indecomposable graded modules of finite length are shown to exist. Some results on the theory of group-graded path algebras and their quotients are used as a basis of their discussion. For this one may see the first author's paper [Trans. Am. Math. Soc. 279, 297-310 (1983; Zbl 0536.16001)].
scientific article; zbMATH DE number 579996