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.