Action du groupe des opérateurs de gamétisation sur les identités ω-polynomiales

The gametization process reduces the study of non-commutative and non-associative algebras satisfying non-homogeneous polynomial identities with variables in X={x1,…,xn} to algebras verifying simpler identities. However after a gametization, certain identities remain invariant and other identities, said universal invariant, are invariant for every gametization. Now in the case n=1, for all algebras satisfying a universal invariant polynomial identity studied until now, we know that the existence of an idempotent is not certain. Using an action of the gametization operators group on the non-commutative and non-associative algebra of polynomials K〈X〉, we give all identities which are invariant and universal invariant by gametization.