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Bell and Zhang have shown that if $A$ and $B$ are two connected gradedalgebras finitely generated in degree one that are isomorphic as ungradedalgebras, then they are isomorphic as graded algebras. We exploit this resultto solve the isomorphism problem in the cases of quantum affine spaces, quantummatrix algebras, and homogenized multiparameter quantized Weyl algebras. Ourresult involves determining the degree one normal elements, factoring out, andthen repeating. This creates an iterative process that allows one to determinerelationships between relative parameters.

The isomorphism problem for quantum affine spaces, homogenized quantized Weyl algebras, and quantum matrix algebras