Attaching a matrix algebra to affine group schemes: polynomial identities

We give a definition of polynomial identities for affine group schemes; over a field F of characteristic 0, the identities of an affine group scheme turn out to coincide with the identities of a certain matrix algebra over F. We prove the identities of an algebraic affine group scheme are those of a matrix algebra whose size is related to the rank of the representative algebra of the group scheme. Moreover, we relate the existence of a polynomial identity of an affine group scheme with the existence of an abelian subgroupscheme of finite index, giving a Passman type result for affine group schemes.