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

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

2011-09-20

arxiv.org/abs/1109.4387v2

Mathematics

Rings and Algebras

v2: Minor changes to organization and correction of typos

Scientific paper

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.

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