  Motivated by the theory of homomorphisms and cv-polynomials of Ore extensions
formulated by several mathematicians, the rol of double Ore extensions
introduced by Zhang and Zhang in the classification of Artin-Schelter regular
algebras of dimension four, and that there are no inclusions between the
classes of all double Ore extensions of an algebra and of all length two
iterated Ore extensions of the same algebra, our aim in this paper is to
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 non-trivial.
We illustrate our results with different examples including Nakayama
automorphisms of trimmed double Ore extensions.
