Title: Higher torsion in p-groups, Casimir operators and
the classifying spectral sequence of a Lie algebra

Authors: Jonathan Pakianathan and Nicholas Rogers

Abstract:
We study exceptional torsion in the integral cohomology of a family of p-groups associated to p-adic Lie algebras.
A spectral sequence E_r^{*,*}[g] is defined for any Lie algebra g which models the Bockstein 
spectral sequence of the corresponding group in characteristic p.  This spectral sequence is then studied for 
complex semisimple Lie algebras like sl_n(C), and the results there are transferred to the c
to the corresponding p-group via the intermediary arithmetic Lie algebra defined over Z.

Over C, it is shown that E_1^{*,*}[g]=H^*(g,U(g)^*)=H^*(\Lambda BG)
where U(g)^* is the dual of the universal enveloping algebra of g and \Lambda BG is the free 
loop space of the classifying space of a Lie group G associated to g.  In characteristic p, a phase transition is observed.  
For example, it is shown that the algebra E_1^{*,*}[sl_2[F_p]] requires at least 17 generators unlike its characteristic zero 
counterpart which only requires two.

Keywords: Lie algebra, cohomology, p-group, free loop space, Bockstein spectral sequence.