We develop here a concept of deformed algebras and their related groups through two examples. 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 Fr��licher Lie groups, and sometimes to Fr��chet Lie groups, that are regular. The first example, indexed by $\mathbb{N},$ is obtained by deformations of the group of bounded classical pseudo-differential operators $Cl^{0,*}$ by algebras of (maybe unbounded) classical pseudo-differential operators. In the second one, the set of indexes is a $\N-$graded groupo��d, which is made of manifolds with boundary that are understood as morphisms of cobordisms. Here again, we get regular Lie groups, and we show how this setting applies to a class of examples that are derived of so-called stochastic cosurfaces.

arXiv admin note: text overlap with arXiv:1402.5629