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arXiv · 2503.03978

Homological properties of some quantum Heisenberg algebras

Samuel A. Lopes·Héctor Suárez·Yésica Suárez
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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 $f, g\in K[t]$. 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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Samuel A. Lopes, Héctor Suárez, Yésica Suárez. 2025-03-05. Homological properties of some quantum Heisenberg algebras. https://arxiv.org/abs/2503.03978

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