The simple non-Lie Malcev algebra as a Lie-Yamaguti algebra

The simple 7-dimensional Malcev algebra $M$ is isomorphic to the irreducible $\mathfrak{s}\mathfrak{l}(2,\mathbb{C})$-module V(6) with binary product $[x,y] = \alpha(x \wedge y)$definedbythe$\mathfrak{sl}(2,$\mathbb{C}$)$-modulemorphism$\alpha\colon \Lambda^2 V(6) \to V(6)$\mathrm{.}Combiningthiswiththeternaryproduct$(x,y,z) = \beta(x \wedge y) \cdot z$definedbythe$\mathfrak{sl}(2,$\mathbb{C}$)$-modulemorphism$\beta\colon \Lambda^2 V(6) \to V(2) \approx \s$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.