Uniform exponential growth in twisted polynomial algebras

Abstract

We consider the growth of a twisted polynomial algebra. We prove that the algebra has polynomially bounded growth if the twisting endomorphism has all eigenvalues of magnitude 0 or 1, and the algebra has uniform exponential growth otherwise.

Keywords:

• Growth in algebras
• twisted polynomial algebra
• uniform exponential growth

MATHEMATICS SUBJECT CLASSIFICATION 2010:

• 16P90

Acknowledgement

The author acknowledges partial support for this work under Embry-Riddle Aeronautical University’s FIRST grant program. The author is grateful to the anonymous referee for comments which improved the quality of the paper.