On GK Dimension and Generator Bounds for a Class of Graded Algebras
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866913685906128896 |
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| author | Kabbaj, Abdourrahmane |
| author_facet | Kabbaj, Abdourrahmane |
| contents | In this paper, we introduce the concept of \textit{monotonic algebras}, a broad class of algebras that includes all Artin-Schelter regular algebras of dimension at most four, as well as algebras with \textit{pure} resolutions, such as Koszul and piecewise Koszul algebras. We show that the Gelfand-Kirillov (GK) dimension of these algebras is bounded above by their global dimension and establish a similar result for the minimal number of generators. Furthermore, we prove a parity theorem for Artin-Schelter regular algebras, demonstrating that the difference between their global dimension and GK dimension is always an even integer. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_11346 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On GK Dimension and Generator Bounds for a Class of Graded Algebras Kabbaj, Abdourrahmane Rings and Algebras In this paper, we introduce the concept of \textit{monotonic algebras}, a broad class of algebras that includes all Artin-Schelter regular algebras of dimension at most four, as well as algebras with \textit{pure} resolutions, such as Koszul and piecewise Koszul algebras. We show that the Gelfand-Kirillov (GK) dimension of these algebras is bounded above by their global dimension and establish a similar result for the minimal number of generators. Furthermore, we prove a parity theorem for Artin-Schelter regular algebras, demonstrating that the difference between their global dimension and GK dimension is always an even integer. |
| title | On GK Dimension and Generator Bounds for a Class of Graded Algebras |
| topic | Rings and Algebras |
| url | https://arxiv.org/abs/2501.11346 |