(1) Department of Mathematics, Rutgers University, Piscataway, NJ, 08854-8019, U.S.A;(2) IME-UFG, CX Postal 131, Goiania –GO, CEP, 74001-970, Brazil
Abstract:
To any directed graph we associate an algebra with edges of the graph as generators and with relations defined by all pairs
of directed paths with the same origin and terminus. Such algebras are related to factorizations of polynomials over noncommutative
algebras. We also construct a basis for our algebras associated to layered graphs.