Hilbert series of algebras associated to directed graphs and order homology |
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Authors: | Vladimir Retakh Shirlei Serconek Robert Wilson |
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Institution: | 1. Department of Mathematics, Rutgers University, Piscataway, NJ 08854-8019, USA;2. IME-UFG, CX Postal 131, Goiania - GO, CEP 74001-970, Brazil |
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Abstract: | We give a homological interpretation of the coefficients of the Hilbert series for an algebra associated with a directed graph and its dual algebra. This allows us to obtain necessary conditions for Koszulity of such algebras in terms of homological properties of the graphs. We use our results to construct algebras with a prescribed Hilbert series. |
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