Where are the N-Koszul algebras of finite global dimension?
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866916208274571264 |
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| author | Kabbaj, Abdourrahmane |
| author_facet | Kabbaj, Abdourrahmane |
| contents | The class of $N$-Koszul graded algebras of finite global dimension has gained lots of attention in recent years, especially in the study of Artin-Schelter regular algebras. While structurally rich and concrete, the only known examples of such algebras are either when $N = 2$, i.e. the algebra is Koszul, or when $N = 3$. Under a mild Hilbert series assumption, we rule out the existence of $N$-Koszul graded algebras of finite global dimension for $N$ not prime. Furthermore, we establish strong restrictions on the global dimension of such algebras. This suggests that perhaps the existence of 3-Koszul algebras with finite global dimension and `nice' Hilbert series is an anomaly. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_10125 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Where are the N-Koszul algebras of finite global dimension? Kabbaj, Abdourrahmane Rings and Algebras The class of $N$-Koszul graded algebras of finite global dimension has gained lots of attention in recent years, especially in the study of Artin-Schelter regular algebras. While structurally rich and concrete, the only known examples of such algebras are either when $N = 2$, i.e. the algebra is Koszul, or when $N = 3$. Under a mild Hilbert series assumption, we rule out the existence of $N$-Koszul graded algebras of finite global dimension for $N$ not prime. Furthermore, we establish strong restrictions on the global dimension of such algebras. This suggests that perhaps the existence of 3-Koszul algebras with finite global dimension and `nice' Hilbert series is an anomaly. |
| title | Where are the N-Koszul algebras of finite global dimension? |
| topic | Rings and Algebras |
| url | https://arxiv.org/abs/2404.10125 |