Published 03 Jul 2006. First received 20 Apr 2006.

Simple Lie algebras of low dimension over GF(2)

Michael Vaughan-Lee

Abstract: 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.

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Appendix A : This appendix contains a MAGMA program to construct the algebras.

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