Two Generator Subalgebras of Lie Algebras
Rings and Algebras
2007-05-23 v1
Abstract
J. G. Thompson showed that a finite group G is solvable if and only if every two -generated subgroup is solvable. Recently, Grunevald, Kunyavskii, Nikolova, and Plotkin have shown that the analogue holds for finite-dimensional Lie algebras over infinite fields of characteristic greater than 5. It is a natural question to ask to what extent the two-generated subalgebras determine the structure of the algebra. It is to this question that this paper is addressed. Here, we consider the classes of strongly-solvable and of supersolvable Lie algebras, and the property of triangulability.
Keywords
Cite
@article{arxiv.0704.2723,
title = {Two Generator Subalgebras of Lie Algebras},
author = {Kevin Bowman and David A. Towers and Vicente R. Varea},
journal= {arXiv preprint arXiv:0704.2723},
year = {2007}
}
Comments
12 pages