The Weil descent functor in the category of algebras with free operators

Abstract

We prove that there exists a version of Weil descent, or Weil restriction, in the category of D-algebras. The objects of this category are k-algebras R equipped with a homomorphism e:R→R⊗kD for some fixed field k and finite-dimensional k-algebra D. We do this under a mild assumption on the so-called associated endomorphisms. In particular, this yields the existence of the Weil descent functor in the category of difference algebras, which, to our knowledge, does not appear elsewhere.