# Self-similar Lie algebras

Journal of the European Mathematical Society (2015)

- Volume: 017, Issue: 12, page 3113-3151
- ISSN: 1435-9855

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topBartholdi, 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 -

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