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Algorithmic construction of Chevalley bases

Part of: Linear algebraic groups and related topics Lie algebras and Lie superalgebras

Published online by Cambridge University Press:  01 December 2012

K. Magaard  and
R. A. Wilson
K. Magaard
Affiliation:
School of Mathematics, University of Birmingham, Birmingham B15 2TT, United Kingdom (email: [email protected])
R. A. Wilson
Affiliation:
School of Mathematical Sciences, Queen Mary, University of London, Mile End Road, London E1 4NS, United Kingdom (email: [email protected])

Abstract

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We present a new algorithm for constructing a Chevalley basis for any Chevalley Lie algebra over a finite field. This is a necessary component for some constructive recognition algorithms of exceptional quasisimple groups of Lie type. When applied to a simple Chevalley Lie algebra in characteristic p⩾5, our algorithm has complexity involving the seventh power of the Lie rank, which is likely to be close to best possible.

MSC classification

Secondary: 17B45: Lie algebras of linear algebraic groups 20G40: Linear algebraic groups over finite fields
Type
Research Article
Information
LMS Journal of Computation and Mathematics , Volume 15 , May 2012 , pp. 436 - 443
Copyright
© The Author(s) 2012

References

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