Bounds for the Entropy of Graded Algebras
Rings and Algebras
2026-05-12 v2
Abstract
Newman, Schneider and Shalev defined the entropy of a graded associative algebra A as H(A) = \limsup_{n \to \infty} \sqrt[n]{a_n}, where a_n is the vector space dimension of the n'th homogeneous component. When A is the homogeneous quotient of a finitely generated free associative algebra, they showed that H(A) \le \sqrt{a_2}. Using some results of Friedland on the maximal spectral radius of 0-1 matrices with a prescribed number of ones, we improve on this bound.
Keywords
Cite
@article{arxiv.math/0209080,
title = {Bounds for the Entropy of Graded Algebras},
author = {Jan Snellman},
journal= {arXiv preprint arXiv:math/0209080},
year = {2026}
}
Comments
4 pages, 1 figure