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

The simple 7-dimensional Malcev algebra M is isomorphic to the irreducible sl(2,C)-module V(6) with binary product [x,y]=α(x∧y) defined by the sl(2,C)-module morphism α:Λ2V(6)→V(6). Combining this with the ternary product (x,y,z)=β(x∧y)⋅z defined by the sl(2,C)-module morphism β:Λ2V(6)→V(2)≈sl(2,C) 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.