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arXiv · 2404.10125

Where are the N-Koszul algebras of finite global dimension?

Abdourrahmane Kabbaj
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Abstract

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.

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Abdourrahmane Kabbaj. 2024-04-15. Where are the N-Koszul algebras of finite global dimension?. https://arxiv.org/abs/2404.10125

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