Growth for Algebras Satisfying Polynomial Identities

الملخص EN

The nth codimension cn(A) of a PI algebra A measures how many identities of degree n the algebra A satisfies.

Growth for PI algebras is the rate of growth of cn(A) as n goes to infinity.

Since in most cases there is no hope in finding nice closed formula for cn(A), we study its asymptotics.

We review here such results about cn(A), when A is an associative PI algebra.

We start with the exponential bound on cn(A) then give few applications.

We review some remarkable properties (integer and half integer) of the asymptotics of cn(A).

The representation theory of the symmetric group Sn is an important tool in this theory.