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Keywords:
graded algebra; structurable algebra; exceptional simple Lie algebra
graded algebra; structurable algebra; exceptional simple Lie algebra
Summary:
We describe two constructions of a certain $\mathbb Z_4^3$-grading on the so-called Brown algebra (a simple structurable algebra of dimension $56$ and skew-dimension $1$) over an algebraically closed field of characteristic different from $2$. The Weyl group of this grading is computed. We also show how this grading gives rise to several interesting fine gradings on exceptional simple Lie algebras of types $E_6$, $E_7$ and $E_8$.
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