On $(n+1)$-ary derivations of simple $n$-ary Mal′tsev algebras

The (n + 1)-ary derivations of simple non-Lie n-ary Maltsev algebras are described in the case of the binary algebra M7 and the ternary algebra M8 .A s a consequence, a description is obtained for the 3-ary derivations of simple non-Lie Maltsev algebras and simple finite-dimensional non-Lie binary-Lie algebras. Exam- ples of semisimple Maltsev algebras having nontrivial 3-ary derivations are given.