Azumaya locus over certain quantum symplectic spaces II

This article undertakes an exploration of a particular variant of multiparameter quantum symplectic algebras, focusing specifically on the quantum Heisenberg algebra at the roots of unity. In this context, the algebra undergoes a transformation into Polynomial Identity algebra, where the dimensions of the simple modules are restricted by their PI degree. We conduct an extensive examination of all possible maximal dimensional simple modules associated with this algebra. Additionally, we present a condition that is both necessary and sufficient for the attainment of maximal dimensional simple modules, thereby facilitating the classification of its Azumaya locus.