Structural properties of the graph algebra K3

The algebras Qn 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 K3 and show that this algebra is Koszul.