Derivations of quantum and involution generalized Weyl algebras

Abstract

In this paper, we classify the derivations of degree-one generalized Weyl algebras over a univariate Laurent polynomial ring. In particular, our results cover the Weyl–Hayashi algebra, a quantization of the first Weyl algebra arising as a primitive factor algebra of [Formula: see text], and a family of algebras which localize to the group algebra of the infinite group with generators [Formula: see text] and [Formula: see text], subject to the relation [Formula: see text]