Construction of some algebras associated to directed graphs and related to factorizations of noncommutative polynomials

Abstract

This is a survey of recently published results. We introduce and study a wide class algebras associated to directed graphs and related to factorizations of noncommutative polynomials. In particular, we show that for many well-known graphs such algebras are Koszul and compute their Hilbert series.

To appear in Proceedings of the Conference "Lie Algebras, Vertex Operator Algebras and Their Applications"