A View Toward Homomorphisms and CV-Polynomials Between Double Ore Extensions

Motivated by the theory of homomorphisms and change-of-variable polynomials (cv-polynomials) of Ore extensions, the role of double Ore extensions in the classification of Artin-Schelter regular algebras of dimension four, and the absence of inclusions between the classes of all double Ore extensions of an algebra and of all two-step iterated Ore extensions of the same algebra, we present a first approach toward a theory of homomorphisms and cv-polynomials between double Ore extensions. We obtain several results on the characterizations of cv-polynomials and their relations with inner derivations of the ring of coefficients of the double algebra, and show that the computation of homomorphisms corresponding to these polynomials is nontrivial. Our results are illustrated with different examples including Nakayama automorphisms of trimmed double Ore extensions.