Self-similar Lie algebras

  • Laurent Bartholdi

    Georg-August-Universität Göttingen, Germany


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

Cite this article

Laurent Bartholdi, Self-similar Lie algebras. J. Eur. Math. Soc. 17 (2015), no. 12, pp. 3113–3151

DOI 10.4171/JEMS/581