ABSTRACT
In this chapter a q-deformation of the generalized Weyl algebra As;h defined in Chapter 8 is introduced. Its generators U and V satisfy UV − qV U = hV s, and it will be denoted by As;h|q. As in the preceding chapters, we will be interested in ordering results for words in the generators U and V . In particular, we introduce associated q-deformed generalized Stirling and Bell numbers and derive some of their properties. As it will turn out, the study of As;h|q is significantly more difficult than the undeformed case, and explicit expressions will be given only for special cases. As in the undeformed case we also introduce a more
general algebra A 〈f〉 h|q where the generators satisfy UV − qV U = hf(V ) for some polynomial
f .
