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

JOURNAL OF ALGEBRA

卷:405

Article

Holdaway, Cody¹  Sisodia, Gautam¹ 

[1] Univ Washington, Dept Math, Seattle, WA 98195 USA

关键词: Quotient category;    Representations of quivers;    Path algebras;    Monomial algebras;    Ufnarovskii graph;   

DOI  :  10.1016/j.jalgebra.2013.12.032

来源: Elsevier

【 摘 要 】

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 QGr A 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 QGr A equivalent to QGr kQ'. A result of Smith now implies that QGr A equivalent to Mod S, the category of right modules over an ultramatricial, hence von Neumann regular, algebra S. (C) 2014 Elsevier Inc. All rights reserved.

【 授权许可】

Free