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A $\mathbb{Z}_4^3$-grading on a 56-dimensional simple structurable algebra and related fine gradings on the simple Lie algebras of type E (1312.1067v1)
Published 4 Dec 2013 in math.RA
Abstract: We describe two constructions of a certain $\mathbb{Z}_43$-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 and 3. We also show how this grading gives rise to several interesting fine gradings on exceptional simple Lie algebras of types E6, E7 and E8.