The entropy of graded algebras

M. F. Newman; Csaba Schneider; Aner Shalev

doi:10.1006/jabr.1999.8053

The entropy of graded algebras

M. F. Newman^*, Csaba Schneider, Aner Shalev

^*Corresponding author for this work

Einstein Institute of Mathematics

Research output: Contribution to journal › Article › peer-review

18 Scopus citations

Abstract

We define the entropy of a graded algebra A=⊕_nA_n by limsup_n→∞dimA_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.

Original language	English
Pages (from-to)	85-100
Number of pages	16
Journal	Journal of Algebra
Volume	223
Issue number	1
DOIs	https://doi.org/10.1006/jabr.1999.8053
State	Published - 1 Jan 2000

Bibliographical note

Funding Information:
During the preparation of this paper we had fruitful discussions with several people. We are grateful to B. Weiss, E. Lindenstrauss, and L. Small for their useful comments and suggestions. A. Shalev is grateful to The Australian National University for its kind hospitality while some of this work was carried out. A. Shalev also acknowledges the support of the BSF Grant No. 96-00101.

Keywords

Entropy
Free Lie algebras
Free associative algebras
Graded Lie algebras
Graded associative algebras
Growth
Hilbert series
Symbolic dynamics

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10.1006/jabr.1999.8053

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KW - Free associative algebras

KW - Graded Lie algebras

KW - Graded associative algebras

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The entropy of graded algebras

Abstract

Bibliographical note

Keywords

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