Year: 2026
Type: preprint
Abstract: In this paper, we consider three growth functions of algebras: the Gelfand-Kirillov dimension, superdimension, and entropy -- as well as a variation of the latter successfully used in the study of Leavitt path algebras. We prove results that make precise the heuristic fact that the Gelfand-Kirillov dimension is suitable for the study of algebras with polynomial growth, the superdimension for algebras with subexponential growth, and the entropy for algebras with exponential growth. We introduce a definition of entropy for graded modules motivated by the entropy for graded algebras. As an application of our study, we give a new criterion for Leavitt path algebras to be PI.
Source: arXiv (Cornell University)
Authors: Schwarz, João, Sebandal, Alfilgen
Language: English
Topic: Rings, Modules, and Algebras
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7213494042