From infinitesimal symmetries to deformed symmetries of Lax-type equations

Deformed algebras: examples and application to Lax equations

We develop here a concept of deformed algebras through three examples and an application. Deformed algebras are obtained from a fixed algebra by deformation along a family of indexes, through formal series. We show how the example of deformed algebra used in \cite{Ma2013} is only an example among others, and how they often give rise to regular Frölicher Lie groups. Then, we show how such deformed algebras arise in a formal integration of Lax equations through time scaling. The infinite dimensional groups under consideration enables to state the uniqueness of the formal solutions, their smooth …