
Chapter 8
A Generalization of the Weyl Algebra
In this chapter we introduce a generalization of the Weyl algebra and consider some related
combinatorial structures, in particular, associated generalized Stirling and Bell numbers.
Recall that we considered in Chapters 5 and 6 the Weyl algebra A
h
defined by two generators
U and V satisfying
UV − VU = h
for some h ∈ C. In Chapter 7 we considered three variants of it: 1) the q-deformed Weyl
algebra A
h|q
where UV − qV U = h, 2) the meromorphic Weyl algebra MA
h
where UV −
VU = hV
2
,and3)theq-deformed meromorphic Weyl algebra MA
h|q
where UV − qV U =
hV
2
. As a common generalization, we will introduce in Chapter 9