On the definition of quasi-Jordan algebra

Velasquez and Felipe recently introduced quasi-Jordan algebras based on the product $a◃b=\frac{1}{2}(a⊣b+b⊢a)$ in an associative dialgebra with operations $⊣$ and $⊢$. We determine the polynomial identities of degree $\le 4$ satisfied by this product. In addition to right commutativity and the right quasi-Jordan identity, we obtain a new associator-derivation identity.