# Category equivalences involving graded modules over weighted path algebras and weighted monomial algebras

- Authors
- Type
- Published Article
- Journal
- Journal of Algebra
- Publication Date
- Jan 01, 2014
- Volume
- 405
- Pages
- 75–91
- Identifiers
- DOI: 10.1016/j.jalgebra.2013.12.032
- Source
- Elsevier
- Keywords
- License
- Unknown

## Abstract

Let k be a field, Q a finite directed graph, and kQ its path algebra. Make kQ an N-graded algebra by assigning each arrow a positive degree. Let I be an ideal in kQ generated by a finite number of paths and write A=kQ/I. Let QGrA denote the quotient of the category of graded right A-modules modulo the Serre subcategory consisting of those graded modules that are the sum of their finite dimensional submodules. This paper shows there is a finite directed graph Q′ with all its arrows placed in degree 1 and an equivalence of categories QGrA≡QGrkQ′. A result of Smith now implies that QGrA≡ModS, the category of right modules over an ultramatricial, hence von Neumann regular, algebra S.