The second quantum Weyl algebra at roots of unity has PI degree n1 n2 times ord(λ^{n1 n2}), and its simple modules split into three torsion types, each explicitly constructed and classified.
Suppose /u1D440is a simple /u1D434(/u1D45E1, /u1D45E2, /u1D706)-module
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Simple Modules over Second Quantum Weyl Algebra
The second quantum Weyl algebra at roots of unity has PI degree n1 n2 times ord(λ^{n1 n2}), and its simple modules split into three torsion types, each explicitly constructed and classified.