Quantized Weyl algebras at roots of unity (Q1650457)

The paper under review describes centers of quantized Weyl algebras in case they are polynomial identity algebras and the authors use this to give a classification of all polynomial identity quantized Weyl algebras that are free over their centers. For the latter algebras their discriminant is computed explicitly and it is also shown that they are locally dominating and effective. Two different proofs are given for the discriminant formula, one based on deformation theory and Poisson geometry and the other uses techniques from quantum cluster algebras. As an application, the automorphism and isomorphism problem is solved for a family of quantized Weyl algebras that are free over their centers and for their tensor products.