Generalizations of Fréchet equations on Lie groups and homogeneous spaces

In this talk, we provide a generalization of polynomials on Lie groups. They are seen as smooth solutions of the Fréchet functional equations naturally generalized on arbitrary groups. On Lie groups, these polynomials are not far from the usual one, but it will be seen that topological or algebraic properties of the group may lead to existence or non-existence of non-constant solutions.