8 papers
Relative Dixmier property for Poisson algebras
Hongdi Huang, Zahra Nazemian, Xin Tang +3
Dixmier property concerns the bijectivity of endomorphisms for algebras. We introduce a relative Dixmier property, which is a generalization of the Dixmier property. This new conce…
Quantum-symmetric equivalence for superpotential algebras
Hongdi Huang, Van C. Nguyen, Kent B. Vashaw +2
We study superpotential algebras by introducing the notion of quantum-symmetric equivalence defined relatively to two fixed Hopf coactions. This concept relies on the non-vanishing…
Relative Cancellation
Hongdi Huang, Zahra Nazemian, Yanhua Wang +1
We introduce and study a relative cancellation property for associative algebras. We also prove a characterization result for polynomial rings which partially answers a question of…
Quantum-symmetric equivalence is a graded Morita invariant
Hongdi Huang, Van C. Nguyen, Padmini Veerapen +2
We show that if two -homogeneous algebras have Morita equivalent graded module categories, then they are quantum-symmetrically equivalent, that is, there is a monoidal equivalen…
Valuation method for Nambu-Poisson algebras
Hongdi Huang, Xin Tang, Xingting Wang +1
Automorphism, isomorphism, and embedding problems are investigated for a family of Nambu-Poisson algebras (or -Lie Poisson algebras) using Poisson valuations.
Group actions on monoidal triangulated categories and Balmer spectra
Hongdi Huang, Kent B. Vashaw
Let be a group acting on a left or right rigid monoidal triangulated category which has a Noetherian Balmer spectrum. We prove that the Balmer spectrum of the cro…
Weighted Poisson polynomial rings in dimension three
Hongdi Huang, Xin Tang, Xingting Wang +1
We discuss Poisson structures on a weighted polynomial algebra defined by a homogeneous element , called a potential. We start with classifying potentia…
Poisson valuations
Hongdi Huang, Xin Tang, Xingting Wang +1
We study Poisson valuations and provide their applications in solving problems related to rigidity, automorphisms, Dixmier property, isomorphisms, and embeddings of Poisson algebra…