Homogamétisation d'algèbres pondérées

We generalize the gametization process introduced in [5]. For this we use not necessarily convex linear combinations of a baric algebra (A,ω) with the gametic algebra defined by the weight ω, we call these combinations homogametizations. After establishing a ponderability condition for a homogametization, we introduce the homogametization operators group and we define two actions of this group on the class of baric algebras and the non-commutative and non-associative algebra K〈X〉 of polynomials with variables in X={x1,…,xn}. When an algebra is defined by an identity, we show that this property is preserved after the group action on the algebra and the identity. We give explicit constructions of elements in K〈X〉 which are invariants or universal invariants for this group action.