Computing Chevalley bases in small characteristics
Rings and Algebras
2011-06-17 v2
Abstract
Let L be the Lie algebra of a simple algebraic group defined over a field F and let H be a split Cartan subalgebra of L. Then L has a Chevalley basis with respect to H. If the characteristic of F is not 2 or 3, it is known how to find it. In this paper, we treat the remaining two characteristics. To this end, we present a few new methods, implemented in Magma, which vary from the computation of centralisers of one root space in another to the computation of a specific part of the Lie algebra of derivations of .
Keywords
Cite
@article{arxiv.0901.1717,
title = {Computing Chevalley bases in small characteristics},
author = {Arjeh M. Cohen and Dan A. Roozemond},
journal= {arXiv preprint arXiv:0901.1717},
year = {2011}
}
Comments
22 pages