Self-similar Lie algebras

Bartholdi, Laurent. "Self-similar Lie algebras." Journal of the European Mathematical Society 017.12 (2015): 3113-3151. <http://eudml.org/doc/277778>.

@article{Bartholdi2015,
abstract = {We give a general definition of branched, 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.},
author = {Bartholdi, Laurent},
journal = {Journal of the European Mathematical Society},
keywords = {groups acting on trees; Lie algebras; wreath products; groups acting on trees; Lie algebras; wreath products},
language = {eng},
number = {12},
pages = {3113-3151},
publisher = {European Mathematical Society Publishing House},
title = {Self-similar Lie algebras},
url = {http://eudml.org/doc/277778},
volume = {017},
year = {2015},
}

TY - JOUR
AU - Bartholdi, Laurent
TI - Self-similar Lie algebras
JO - Journal of the European Mathematical Society
PY - 2015
PB - European Mathematical Society Publishing House
VL - 017
IS - 12
SP - 3113
EP - 3151
AB - We give a general definition of branched, 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.
LA - eng
KW - groups acting on trees; Lie algebras; wreath products; groups acting on trees; Lie algebras; wreath products
UR - http://eudml.org/doc/277778
ER -