In this study in the space R®, the cross-product was defined as analogous vector-product in R3. We showed that this product makes R3 a Lie algebra. Therefore, it was showed that the Lie algebras (R®,0) and (A4, [,]) are isomorphic. As a generalization, in the space of dimension m — n (n -l)/2, cross-product can be given as Rm x Rm -> Rm , xoy = J” 1 [J(X), J(Y)] where J — Rm -> An is Lie algebra isomorphism. At the end, we showed that the cross - product we defined is vector product well known for n = 3.