Abstract
From an octonion algebra [Formula: see text] over a field [Formula: see text] of characteristic not two or three, we show that the fundamental representation [Formula: see text] of the derivation algebra [Formula: see text] and the spinor representation [Formula: see text] of [Formula: see text] are special orthogonal representations. They have particular geometric properties coming from their similarities with binary cubics and we show that the covariants of these representations and their Mathews identities are related to the Fano plane and the affine space [Formula: see text]. This also permits to give constructions of exceptional Lie superalgebras.
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