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

Alessio Marrani; Piero Truini

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

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arxiv 1506.04604 v3 pith:Z5YNZZEE submitted 2015-06-15 math.RA hep-thmath.RT

Alessio Marrani , Piero Truini This is my paper · ORCID

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keywords mathbfalgebraconstructionfrac12matricessextonionszornalgebraically

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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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Exceptional Periodicity and Magic Star Algebras. I : Foundations
math.RT 2019-09 conditional novelty 5.0 of 10

The paper rigorously defines 'Magic Star algebras', periodic finite dimensional generalizations of e6, e7, and e8, which are Lie algebras only at the base level n=1.

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