The Koszul dual of the ring of three commuting matrices - Hreinsdóttir, Freyja (Mathematica Scandinavica, 2000)
Let X=(x_ij), Y=(y_ij) and Z=(z_ij) be generic n by n matrices. Let k be a field with char k eq 2, 3, S=k[x_11, … , x_nn, y_11, … , y_nn, z_11, … , z_nn] and let I be the ideal generated by the entries of the matrices XY-YX, XZ-ZX and YZ-ZY. We study the Koszul dual of the ring R=S/I and show that for n≥ 3 this is the enveloping algebra of a nilpotent Lie algebra. We also give the dimension of the Lie algebra in each degree.