The koszul dual of the ring of commuting matrices

Abstract

Let X={x_ij} and Y={y_ij} be generic n by n matrices and Z = XY –YX. Let where k is a field with char K ≠ 2 and let I be the ideal generated by the entries of Z. Denote by R the quotient ring S/I. In this paper we study its Koszul dual, which is the algebra generated by and denoted by R ^!, and show that for n≥3 it is the enveloping algebra of a nilpotent Lie algebra.