Article ID Journal Published Year Pages File Type
4668386 Advances in Mathematics 2006 37 Pages PDF
Abstract

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 octonions. Using the sextonions, we show similar results hold for the rows of an expanded Freudenthal magic chart. We also obtain new interpretations of the adjoint variety of the exceptional group G2.

Related Topics
Physical Sciences and Engineering Mathematics Mathematics (General)