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Sextonions and the magic square. (English) Zbl 1154.17304
Summary: 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.

MSC:
17B60 Lie (super)algebras associated with other structures (associative, Jordan, etc.)
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