Homological properties of some quantum Heisenberg algebras
Abstract
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.
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