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SEXTONIONS AND THE MAGIC SQUARE

Published online by Cambridge University Press:  24 April 2006

BRUCE W. WESTBURY
BRUCE W. WESTBURY
Affiliation:
Mathematics Institute, University of Warwick, Coventry CV4 7AL, United [email protected]
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Abstract

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.

Keywords

17B60
Type
Notes and Papers
Information
Journal of the London Mathematical Society , Volume 73 , Issue 2 , April 2006 , pp. 455 - 474
Copyright
The London Mathematical Society 2006

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