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Simple Lie Algebras of Low Dimension Over GF (2)

Published online by Cambridge University Press:  01 February 2010

Michael Vaughan-Lee
Michael Vaughan-Lee
Affiliation:
Christ Church, Oxford 0X1 1DP, United Kingdom, vlee@maths.ox.ac.uk

Abstract

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We classify the simple Lie algebras of dimension at most 9 over GF(2). There is one of dimension 3 and one of dimension 6, there are two of dimension 7 and two of dimension 8, and there is one of dimension 9. The two simple Lie algebras of dimension 8 are restricted Lie algebras. If we extend the ground field to GF(4), then the six-dimensional algebra is no longer simple, and if we extend the ground field to GF(8) then the nine-dimensional algebra is no longer simple. But the other algebras are all central simple.

Information

Type
Research Article
Information
LMS Journal of Computation and Mathematics , Volume 9 , 2006 , pp. 174 - 192
Copyright
Copyright © London Mathematical Society 2006

References

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Supplementary material: File

JCM 9 Lee Appendix A

Lee Appendix A

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