Self-similar Lie algebras
Rings and Algebras
2016-06-28 v1 Group Theory
Abstract
We give a general definition of self-similar Lie algebras, and show that important examples of Lie algebras fall into that class. We give sufficient conditions for a self-similar Lie algebra to be nil, and prove in this manner that the self-similar algebras associated with Grigorchuk's and Gupta-Sidki's torsion groups are nil as well as self-similar. We derive the same results for a class of examples constructed by Petrogradsky, Shestakov and Zelmanov.
Keywords
Cite
@article{arxiv.1003.1125,
title = {Self-similar Lie algebras},
author = {Laurent Bartholdi},
journal= {arXiv preprint arXiv:1003.1125},
year = {2016}
}