Generalizations Of n-Leibniz Algebras And n-Lie Algebras

In general, Lie algebras are vector spaces equipped with an alternating, bilinear product that obeys the Jacobi identity, a sort of product rule. We first explore Leibniz algebras, generalizations of Lie algebras in which the bilinear product is no longer required to be alternating. Then, we will extend our discussion to n-airy operations and see what connections we can make to n-Leibniz and n-Lie algebras.