Abstract

This is a survey of recently published results. We introduce and study a wide class of 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. Let R be an associative ring with unit and P(t) = a0t n +a1t n−1 +� � � +an be a polynomial over R. Here t is an independent central variable. We consider factorizations of P(t) into a product

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