The algebras Q n describe the relationship between the roots and coefficients of a non-commutative polynomial. Gelfand et al. (2001a) have defined quotients of these algebras corresponding to graphs. In this work we construct the class of algebras corresponding to the n-vertex path, P n . We then show these algebras are Koszul and find a formula for their Hilbert series.
The algebras Q n describe the relationship between the roots and coefficients of a non-commutative polynomial. I. Gelfand, S. Gelfand, and V. Retakh have defined quotients of these algebras corresponding to graphs. In this paper we find the Hilbert series of the class of algebras corresponding to the graph K 3 and show that this algebra is Koszul.
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