Table of Contents
ISRN Algebra
Volume 2012 (2012), Article ID 170697, 26 pages
http://dx.doi.org/10.5402/2012/170697
Review Article

Growth for Algebras Satisfying Polynomial Identities

Mathematics Department, The Weizmann Institute, 76100 Rehovot, Israel

Received 6 September 2012; Accepted 25 September 2012

Academic Editors: E. Aljadeff and F. Marko

Copyright © 2012 Amitai Regev. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

The th codimension of a PI algebra measures how many identities of degree the algebra satisfies. Growth for PI algebras is the rate of growth of as goes to infinity. Since in most cases there is no hope in finding nice closed formula for , we study its asymptotics. We review here such results about , when is an associative PI algebra. We start with the exponential bound on then give few applications. We review some remarkable properties (integer and half integer) of the asymptotics of . The representation theory of the symmetric group is an important tool in this theory.