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arXiv · 1010.6295

Hilbert series of algebras associated to direct graphs and order homology

Vladimir Retakh·Shirlei Serconek·Robert Wilson
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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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Vladimir Retakh, Shirlei Serconek, Robert Wilson. 2010-10-29. Hilbert series of algebras associated to direct graphs and order homology. https://arxiv.org/abs/1010.6295

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