Bounds for the entropy of graded algebras
Abstract
Newman, Schneider and Shalev defined the entropy of a graded associative algebra A as H(A)=limsupn→∞ann, where an is the vector space dimension of the n’th homogeneous component of A. When A is the homogeneous quotient of a finitely generated free associative algebra, they showed that H(A)≤a2. Using some results of Friedland on the maximal spectral radius of (0,1)-matrices with a prescribed number of 1’s, we improve on this bound.
Fields of Study & Subjects
Advanced Topics in Algebra
Matrix Theory and Algorithms
Algebraic structures and combinatorial models
Publication details
- Journal / source
- Communications in Algebra
- Pages
- 1–7
- Publication date
- 8 May 2026
- Language
- EN