Self-similar Lie algebras

Details Self-similar Lie algebras Self-similar Lie algebras

2010-03-04

arxiv.org/abs/1003.1125v1

Mathematics

Rings and Algebras

Scientific paper

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.

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