  Generalized Weyl Algebras (GWAs) appear in diverse areas of mathematics
including mathematical physics, noncommutative algebra, and representation
theory. We study the invariants of quantum GWAs under finite automorphisms. We
extend a theorem of Jordan and Wells and apply it to determine the fixed ring
of quantum GWAs under diagonal automorphisms. We further study properties of
the fixed rings, including global dimension, rigidity, and simplicity.
