Self-similar Lie algebras

被引：9

作者：

Bartholdi, Laurent ^{[1
]}

机构：

[1] Univ Gottingen, Math Inst, D-37073 Gottingen, Germany

来源：

JOURNAL OF THE EUROPEAN MATHEMATICAL SOCIETY | 2015年 / 17卷 / 12期

关键词：

Groups acting on trees; Lie algebras; wreath products; MAXIMAL CLASS; GROWTH; EXAMPLES; RINGS;

D O I：

10.4171/JEMS/581

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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.

引用

页码：3113 / 3151

页数：39

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