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A 4 3 -grading on a 56 -dimensional simple structurable algebra and related fine gradings on the simple Lie algebras of type E

Diego Aranda-OrnaAlberto ElduqueMikhail Kochetov — 2014

Commentationes Mathematicae Universitatis Carolinae

We describe two constructions of a certain 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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