Groups of formal diffeomorphisms of the superline, generating functions for sequences of polynomials, and functional equations

One of the goals in this article is to extend the umbral calculus to sequences of superpolynomials. A study is made of the group of formal diffeomorphisms of the superline and its main subgroups (the umbral group, the group of formal diffeomorphisms of the line). A complete description of the one-parameter subgroups is obtained, and a faithful supermatrix representation of this group is constructed. Homogeneous coalgebras on the line and superline are studied. The class of nondegenerate homogeneous coalgebras on the line is completely described. Functional equations that are connected with these coalgebras and generalize the classical functional equations of Cauchy, Pexider, Abel, Levi–Civita, and Stäkel are introduced and solved.
Bibliography: 30 titles.