Isomorphisms of some quantum spaces

Abstract

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.

To appear in the the proceedings of the 31st Ohio State-Denison conference (Contemp. Math.). We include a supplementary appendix with a result on isomorphisms of quantum affine spaces

References in corpus (1)

• Automorphisms and isomorphism of quantum generalized Weyl algebras

Cited by in corpus (9)

• The isomorphism problem for quantum affine spaces, homogenized quantized Weyl algebras, and quantum matrix algebras
• Two-generated algebras and standard-form congruence
• The isomorphism problem for multiparameter quantized Weyl algebras
• The Zariski cancellation problem for Poisson algebras
• Classification of twisted generalized Weyl algebras over polynomial rings
• Isomorphisms of graded path algebras
• Graded automorphisms of quantum affine spaces
• Some algebras similar to the 2x2 Jordanian matrix algebras
• Stabilizing Automorphisms of Quantum Affine Space