Sextonions and the Magic Square
نویسنده
چکیده
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.
منابع مشابه
The Sextonions and E 7
We fill in the “hole” in the exceptional series of Lie algebras that was observed by Cvitanovic, Deligne, Cohen and deMan. More precisely, we show that the intermediate Lie algebra between e7 and e8 satisfies some of the decomposition and dimension formulas of the exceptional simple Lie algebras. A key role is played by the sextonions, a six dimensional algebra between the quaternions and octon...
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