  We consider a series of questions that grew out of determining when two
quantum planes are isomorphic. In particular, we consider a similar question
for quantum matrix algebras and certain ambiskew polynomial rings.
Additionally, we modify a result by Alev and Dumas to show that two quantum
Weyl algebras are isomorphic if and only if their parameters are equal or
inverses of each other.

Quantum Algebra;Rings and Algebras