2024/04/15 by Kabbaj, Abdourrahmane
#FOS: Mathematics #Rings and Algebras (math.RA)
paper · doi:10.48550/arxiv.2404.10125
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.