Semisimplicity of the Deformations of the Subcharacter Algebra of an Abelian Group

For those deformations that satisfy a certain non-degeneracy condition, we describe the structure of simple modules subcharacter algebra finite group. abelian groups, prove deformation given by inclusion natural numbers, which corresponds to generated fibred bisets over field characteristic zero, is not semisimple. In cyclic group prime order case, provide complete description semisimple deformations.