Homological properties of some quantum Heisenberg algebras
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866909894539476992 |
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| author | Lopes, Samuel A. Suárez, Héctor Suárez, Yésica |
| author_facet | Lopes, Samuel A. Suárez, Héctor Suárez, Yésica |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_03978 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Homological properties of some quantum Heisenberg algebras Lopes, Samuel A. Suárez, Héctor Suárez, Yésica Rings and Algebras 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. |
| title | Homological properties of some quantum Heisenberg algebras |
| topic | Rings and Algebras |
| url | https://arxiv.org/abs/2503.03978 |