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Structurable algebras and groups of type E_6 and E_7

R. Skip Garibaldi
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Abstract

It is well-known that every algebraic group of type F_4 is the automorphism group of an exceptional Jordan algebra, and that up to isogeny all groups of type ^1E_6 with trivial Tits algebras arise as the isometry groups of norm forms of such Jordan algebras. We describe a similar relationship between groups of type E_6 and groups of type E_7 and use it to give explicit descriptions of the homogeneous projective varieties associated to groups of type E_7 with trivial Tits algebras. The underlying algebraic structure for the relationship considered here are a sort of 56-dimensional structurable algebra which are forms of an algebra constructed from an exceptional Jordan algebra.

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R. Skip Garibaldi. 1999-12-14. Structurable algebras and groups of type E_6 and E_7. https://doi.org/10.1006/jabr.1998.7584

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