42 research outputs found
Limits over categories of extensions
We consider limits over categories of extensions and show how certain
well-known functors on the category of groups turn out as such limits. We also
discuss higher (or derived) limits over categories of extensions.Comment: 18 page
Lie Dimension Subrings
We compare, for L a Lie ring over the integers, its lower central series
(\gamma_n(L))_{n>0} and its dimension series defined by \delta_n(L):=L\cap
\varpi^n(L) in the universal enveloping algebra of L. We show that
\gamma_n(L)=\delta_n(L) for all n<4, but give an example showing that they may
differ if n=4. We introduce simplicial methods to describe these results, and
to serve as a possible tool for further study of the dimension series.Comment: Small typos fixed wrt v