English

Lie Dimension Subrings

Rings and Algebras 2015-12-14 v2 Group Theory

Abstract

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.

Keywords

Cite

@article{arxiv.1308.2118,
  title  = {Lie Dimension Subrings},
  author = {Laurent Bartholdi and Inder Bir S. Passi},
  journal= {arXiv preprint arXiv:1308.2118},
  year   = {2015}
}

Comments

Small typos fixed wrt v1

R2 v1 2026-06-22T01:06:52.721Z