Derivations of Quantum and Involution Generalized Weyl Algebras

Abstract

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 $U_q^{+}({\mathfrak{so}}_5)$, and a family of algebras which localize to the group algebra of the infinite group with generators $x$ and $y$, subject to the relation $xy=y^{-1}x.$

16 pages

References in corpus (1)

• Automorphisms and isomorphism of quantum generalized Weyl algebras