Document Zbl 1154.17304

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Sextonions and the magic square. (English) Zbl 1154.17304

J. Lond. Math. Soc., II. Ser. 73, No. 2, 455-474 (2006).

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.

Cited in 17 Documents

MSC:

17B60

Lie (super)algebras associated with other structures (associative, Jordan, etc.)

Keywords:

six-dimensional subalgebra of the split octonions

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