An equivalence of categories for graded modules over monomial algebras and path algebras of quivers

JOURNAL OF ALGEBRA

卷:353

Article

Holdaway, Cody¹  Smith, S. Paul¹ 

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

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

DOI  :  10.1016/j.jalgebra.2011.11.033

来源: Elsevier

【 摘 要 】

Let A be a finitely generated connected graded k-algebra defined by a finite number of monomial relations, or, more generally, the path algebra of a finite quiver modulo a finite number of relations of the form path = 0. Then there is a finite directed graph, Q, the Ufnarovskii graph of A, for which there is an equivalence of categories QGr A QGr(kQ). Here OGrA is the quotient category GrA/Fdim of graded A-modules modulo the subcategory consisting of those that are the sum of their finite dimensional submodules. The proof makes use of an algebra homomorphism A -> kQ that may be of independent interest. (C) 2011 Elsevier Inc. All rights reserved.

【 授权许可】

Free