2025/03/05 by Lopes, Samuel A., Suárez, Héctor, Suárez, Yésica
#FOS: Mathematics #Rings and Algebras (math.RA)
paper · doi:10.48550/arxiv.2503.03978
In this paper we study the properties Koszul, Artin-Schelter regular and (skew) Calabi-Yau of some special types of quantum and generalized Heisenberg algebras and also analyze relations between these algebras, (graded) iterated Ore extensions and (graded) skew PBW extensions. The first-named author and Razavinia introduced the quantum generalized Heisenberg algebras, which depend on a parameter q and two polynomials f, g∈ K[t]. We prove that under certain conditions for f, g these algebras are Koszul, Artin-Shelter regular, Calabi-Yau and graded Calabi-Yau.