Torsion table for the lie algebra

Abstract

We study the Lie ring of all strictly upper-triangular matrices with entries in . Its complete homology for is computed. We prove that every pm-torsion appears in for . For , Dwyer proved that the bound is sharp, i.e., there is no p-torsion in when prime . In general, for the bound is not sharp, as we show that there is 8-torsion in . As a sideproduct, we derive the known result, that the ranks of the free part of are the Mahonian numbers (=number of permutations of with k inversions), using a different approach than Kostant. Furthermore, we determine the algebra structure (cup products) of .