Maximal subalgebras of exceptional Jordan algebras
The maximal subalgebras of simple finite dimensional exceptional quadratic Jordan algebras are obtained, thereby completing the classification begun in [J. Algebra 30, 155--180 (1974; Zbl 0282.17009)]. The methods used are those of structure theory and the author's classification of point-spaces in exceptional quadratic Jordan algebras (cf. the following review Zbl 0358.17019). The structure of the maximal subalgebras is studied and in particular a 16 dimensional exceptional algebra is exhibited. This is no longer the smallest exceptional algebra known to the author. Using McCrimmon's Peirce \(S\)-identities, one can construct an exceptional algebra of dimension \(12\).
scientific article; zbMATH DE number 3558017