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Sextonions, Zorn Matrices, and $\mathbf{e_{7 \frac12}}$ (1506.04604v3)
Published 15 Jun 2015 in math.RA, hep-th, and math.RT
Abstract: By exploiting suitably constrained Zorn matrices, we present a new construction of the algebra of sextonions (over the algebraically closed field $\mathbb{C}$). This allows for an explicit construction, in terms of Jordan pairs, of the non-semisimple Lie algebra $\mathbf{e_{7 \frac12}}$, intermediate between $\mathbf{e_{7}}$ and $\mathbf{e_{8}}$, as well as of all Lie algebras occurring in the sextonionic row and column of the extended Freudenthal Magic Square.