The entropy of graded algebras

JOURNAL OF ALGEBRA

卷:223

Article

Newman, MF ; Schneider, C

关键词: free associative algebras;    free Lie algebras;    graded associative algebras;    graded Lie algebras;    entropy;    Hilbert series;    growth;    symbolic dynamics;   

DOI  :  10.1006/jabr.1999.8053

来源: Elsevier

【 摘 要 】

We define the entropy of a graded algebra A = +(n) A(n) by lim sup(n-->infinity) n root dim A(n). This is related to the notion of entropy in symbolic dynamics, and could serve as a natural dimension concept for algebras with exponential growth. We study the entropy of quotients and subalgebras of free associative algebras and free Lie algebras. We also study the behavior of the entropy function under free products, and obtain several characterizations of free algebras in terms of entropy. (C) 2000 Academic Press.

【 授权许可】

Free