  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 work we find the Hilbert series of the class of algebras corresponding to
the graph $K_3$. We also show this algebra is Koszul using the lattice
definition.
