Twisted Traces and Positive Forms on Generalized $q$-Weyl Algebras

Daniil Klyuev

Let $\mathcal{A}$ be a generalized $q$-Weyl algebra, it is generated by $u$, $v$, $Z$, $Z^{-1}$ with relations $Zu{Z}^{-1}=q^{2}u$, $Zv{Z}^{-1}=q^{-2}v$, $uv=P\left(q^{-1}Z\right)$, $vu=P(…