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Journal of the London Mathematical Society 2006 73(2):455-474; doi:10.1112/S0024610706022605
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© The London Mathematical Society

Sextonions and the Magic Square

Bruce W. Westbury

Mathematics Institute, University of Warwick Coventry CV4 7AL, United Kingdom bww{at}maths.warwick.ac.uk

Received 11 October 2004. Revision received 17 March 2005.

Associated to any complex simple Lie algebra is a non-reductive complex Lie algebra which we call the intermediate Lie algebra. We propose that these algebras can be included in both the magic square and the magic triangle to give an additional row and column. The extra row and column in the magic square correspond to the sextonions. This is a six-dimensional subalgebra of the split octonions which contains the split quaternions.


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