Geodesic
Self-similar Lie algebras
Journal of the European Mathematical Society, Tome 17 (2015) no. 12, pp. 3113-3151 Cet article a éte moissonné depuis la source EMS Press

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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
DOI : 10.4171/jems/581
Classification : 20-XX, 16-XX, 17-XX
Keywords: Groups acting on trees, Lie algebras, wreath products 
@article{JEMS_2015_17_12_a4,
     author = {Laurent Bartholdi},
     title = {Self-similar {Lie} algebras},
     journal = {Journal of the European Mathematical Society},
     pages = {3113--3151},
     year = {2015},
     volume = {17},
     number = {12},
     doi = {10.4171/jems/581},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/jems/581/}
}
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Laurent Bartholdi. Self-similar Lie algebras. Journal of the European Mathematical Society, Tome 17 (2015) no. 12, pp. 3113-3151. doi: 10.4171/jems/581

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