The isomorphism problem for quantum affine spaces, homogenized quantized Weyl algebras, and quantum matrix algebras
arXiv:1605.08711 · doi:10.1016/j.jpaa.2016.12.036
Abstract
Bell and Zhang have shown that if and are two connected graded algebras finitely generated in degree one that are isomorphic as ungraded algebras, then they are isomorphic as graded algebras. We exploit this result to solve the isomorphism problem in the cases of quantum affine spaces, quantum matrix algebras, and homogenized multiparameter quantized Weyl algebras. Our result involves determining the degree one normal elements, factoring out, and then repeating. This creates an iterative process that allows one to determine relationships between relative parameters.
Clarifications and corrections throughout. Section 5 has been reorganized with a new proof for Lemma 5.4. To appear in Journal of Pure and Applied Algebra
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