Construction of Chevalley Bases of Lie Algebras

Dan Roozemond

Lie algebras are often used to study the algebraic groups from which they originate, but they are interesting objects in their own right as well. For (almost) every simple Lie algebra there exists a particular basis with special properties, invented by Chevalley: an extremely useful tool to study such algebras.

Algorithms exist and have been implemented to, given a Lie algebra in some way, compute its Chevalley basis. Unfortunately, these algorithms break down in some special cases, in particular over fields of characteristic 2 and 3. We give an overview of the difficulties that arise in these small characteristics, present some solutions, and show how this approach highlights special properties of those Lie algebras.

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