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

Abstract

Let A be a finitely generated connected graded k-algebra defined by a finite number of monomial relations. Then there is a finite directed graph, Q, the Ufnarovskii graph of A, for which the categories QGr(A) and QGr(kQ) are equivalent: QGr(A) denotes the quotient category of graded A-modules modulo the subcategory consisting of those that are the sum of their finite dimensional submodules; QGr(kQ) has a similar definition. The proof makes use of an algebra homomorphism A--->kQ that may be of independent interest.