Torsion table for the Lie algebra nil_n 

We study the Lie ring nil_n of all strictly upper-triangular n\times n matrices with entries in Z. Its complete homology for n<=8 is computed.
We prove that every p^m-torsion appears in H_*(nil_n;Z) for p^m<=n-2. For m=1, Dwyer proved that the bound is sharp, i.e. there is no p-torsion in H_*(nil_n;Z) when prime p>n-2. In general, for m>1 the bound is not sharp, as we show that there is 8-torsion in H_*(nil_8;Z).
As a sideproduct, we derive the known result, that the ranks of the free part of H_\*(nil_n;Z) are the Mahonian numbers (=number of permutations of [n] with k inversions), using a different approach than Kostant. Furthermore, we determine the algebra structure (cup products) of H^*(nil_n;Q).