Quaternions, octonions and the forms of the exceptional simple classical Lie superalgebras (Q1424246)

In this article the forms of the exceptional simple classical Lie superalgebras \(G(3)\), \(F(4)\), and \(D(2,1; \alpha)\) are determined up to equivalence over fields of characteristic \(\not=\) 2, 3. This reduces to the problem of determining which forms of their even parts admit an absolutely irreducible and faithful representation of dimension 14, 16, and 8, respectively. All these forms are intimately related to quaternion or octonion algebras. A final section gives the classification up to isomorphism of the real forms of these superalgebras.