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

Bell and Zhang have shown that if $A$ and $B$ 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.Comment: 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 Algebr

Isomorphisms of some quantum spaces

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.Comment: 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 space

Gender discourse, awareness, and alternative responses for men in everyday living

In this paper, the authors use examples from their experiences to explore the nuances and complexities of contemporary gender practices. They draw on discourse and positioning theories to identify the ways in which culturally dominant, and difficult to notice, gender constructions help shape everyday experiences. In addition, the authors share their view that there are benefits in developing skills in noticing contemporary practices made available by dominant gender constructions. Such noticing expands possibilities for ways of responding and relating that might produce outcomes for men and women that fit with their hopes for living

Discriminants of Taft algebra smash products and applications

A general criterion is given for when the center of a Taft algebra smash product is the fixed ring. This is applied to the study of the noncommutative discriminant. Our method relies on the Poisson methods of Nguyen, Trampel, and Yakimov, but also makes use of Poisson Ore extensions. Specifically, we fully determine the inner faithful actions of Taft algebras on quantum planes and quantum Weyl algebras. We compute the discriminant of the corresponding smash product and apply it to compute the Azumaya locus and restricted automorphism group.Comment: Small typos corrected. To appear in Algebras and Representation Theory. V2:Revisions throughout. Section 4 is now contained primarily in the appendi