 Generalized Weyl algebra

For a ring $D$, an automorphism $\sigma$ and central $t$, adjoin $X,Y$ with $Xd=\sigma (d)X$, $Yd={\sigma }^{-1}(d)Y$, $YX=t$ and $XY=\sigma (t)$. This construction includes Weyl algebras and rank-one universal enveloping algebras.