  The simple 7-dimensional Malcev algebra $M$ is isomorphic to the irreducible
$\mathfrak{sl}(2,\mathbb{C})$-module V(6) with binary product $[x,y] = \alpha(x
\wedge y)$ defined by the $\mathfrak{sl}(2,\mathbb{C})$-module morphism
$\alpha\colon \Lambda^2 V(6) \to V(6)$. Combining this with the ternary product
$(x,y,z) = \beta(x \wedge y) \cdot z$ defined by the
$\mathfrak{sl}(2,\mathbb{C})$-module morphism $\beta\colon \Lambda^2 V(6) \to
V(2) \approx \s$ gives $M$ the structure of a generalized Lie triple system, or
Lie-Yamaguti algebra. We use computer algebra to determine the polynomial
identities of low degree satisfied by this binary-ternary structure.
