Derivations of quantum and involution generalized Weyl algebras

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 U-q(+) (so5), and a family of algebras which localize to the group algebra of the infinite group with generators x and y, subject to the relation xy = y(-1)x.