On GK Dimension and Generator Bounds for a Class of Graded Algebras

2025/01/20 by Kabbaj, Abdourrahmane
#FOS: Mathematics #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.2501.11346

Abstract

In this paper, we introduce the concept of monotonic algebras, a broad class of algebras that includes all Artin-Schelter regular algebras of dimension at most four, as well as algebras with 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.

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