Abstract
Automorphisms of order 2 are studied in order to understand generalized symmetric spaces. The groups of type \({{\mathrm{E}}}_6\) we consider here can be realized as both the group of linear maps that leave a certain determinant invariant, and also as the identity component of the automorphism group of a class of structurable algebras known as Brown algebras. We will classify the k-involutions of these groups of type \({{\mathrm{E}}}_6\) using aspects of both descriptions.
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Hutchens, J. Isomorphism classes of k-involutions of algebraic groups of type \({{\mathrm{E}}}_6\) . Beitr Algebra Geom 57, 525–552 (2016). https://doi.org/10.1007/s13366-016-0280-z
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DOI: https://doi.org/10.1007/s13366-016-0280-z