Commutator identities of the homotopes of $(-1,1)$-algebras

We study the commutator algebras of the homotopes of $(-1,1)$-algebras and prove that they are Malcev algebras satisfying the Filippov identity $h_\alpha(x,y,z)=0$ in the case of strictly $(-1,1)$-algebras. We also proved that every Malcev algebra with the identities $xy^3=0$, $xy^2z^2=0$ and $h_\alpha(x,y,z)=0$ is nilpotent of index at most 6.