Almost-simple affine difference algebraic groups (Q2231141)

Affine algebraic groups can be described as subgroups of a general linear group defined by polynomials in the matrix entries. Affine difference algebraic groups can be described as subgroups of a general linear group defined by difference polynomials in the matrix entries, i.e., the defining equations involve a formal symbol \(\sigma\) that has to be interpreted as a ring endomorphism. The author shows that isomorphism theorems from abstract group theory have meaningful analogs for these groups and that one can establish a Jordan-Hölder type theorem that allows to decompose any affine difference algebraic group into almost-simple affine difference algebraic groups. The author also characterizes almost-simple affine difference algebraic groups via almost-simple affine algebraic groups.