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arXiv · 1506.04604

Sextonions, Zorn Matrices, and $\mathbf{e_{7 \frac12}}$

Alessio Marrani·Piero Truini
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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.

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BibTeXRIS

Alessio Marrani, Piero Truini. 2017-05-20. Sextonions, Zorn Matrices, and $\mathbf{e_{7 \frac12}}$. https://doi.org/10.1007/s11005-017-0966-7

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