On the right-symmetric algebras with a unital matrix subalgebra

Under study are the right-symmetric algebras over a field $F$ which possess a “unital” matrix subalgebra $M_n(F)$. We classify all these finite-dimensional right-symmetric algebras $\mathcal{A}=W\oplus M_2(F)$ in the case when $W$ is an irreducible module over $sl_2(F)$.