A New Division Algebra Representation of $E_7$

Tevian Dray, Corinne A. Manogue, Robert A. Wilson

We decompose the Lie algebra ${\mathfrak{e}}_{8(-24)}$ into representations of ${\mathfrak{e}}_{7(-25)}\oplus \mathfrak{sl}(2,\mathbb{R})$ using our recent description of $\mathfrak{e}_…