On differential smoothness of certain Artin-Schelter regular algebras of dimension 5
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arXiv
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866914296915558400 |
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| author | Rubiano, Andrés |
| author_facet | Rubiano, Andrés |
| contents | This article investigates the differential smoothness of various five-dimensional Artin-Schelter regular algebras. By analyzing the relationship between the number of generators and the Gelfand-Kirillov dimension, we provide structural obstructions to differential smoothness in specific algebraic families. In particular, we prove that certain two- and four-generator AS-regular algebras of global dimension five fail to admit a differential calculus, while a five-generator graded Clifford algebra provides a contrasting positive example. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_10853 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On differential smoothness of certain Artin-Schelter regular algebras of dimension 5 Rubiano, Andrés Rings and Algebras Differential Geometry 16E45, 16S30, 16S32, 16S36, 16T05, 16W50, 18G10, 58B34 This article investigates the differential smoothness of various five-dimensional Artin-Schelter regular algebras. By analyzing the relationship between the number of generators and the Gelfand-Kirillov dimension, we provide structural obstructions to differential smoothness in specific algebraic families. In particular, we prove that certain two- and four-generator AS-regular algebras of global dimension five fail to admit a differential calculus, while a five-generator graded Clifford algebra provides a contrasting positive example. |
| title | On differential smoothness of certain Artin-Schelter regular algebras of dimension 5 |
| topic | Rings and Algebras Differential Geometry 16E45, 16S30, 16S32, 16S36, 16T05, 16W50, 18G10, 58B34 |
| url | https://arxiv.org/abs/2507.10853 |