Аңдатпа
Let V n = ⟨e 1,…, e n+1⟩ be the vector product n-Lie algebra with n-Lie commutator [e 1,…, ˆe i ,…, e n+1] = (− 1) i e i over the field of complex numbers. Any finite-dimensional n-Lie V n -module is completely reducible. Any finite- dimensional irreducible n-Lie V n -module is isomorphic to an n-Lie extension of s o n+1-module with highest weight tπ1 for some nonnegative integer t.