Growth for Algebras Satisfying Polynomial Identities. (21st November 2012)

• Record Type: Journal Article
• Authors: Regev, Amitai
• Other Names: Aljadeff E. Academic Editor.; Marko F. Academic Editor.
• Is Part Of: ISRN algebra. Volume 2012(2012)
• Publication Date: 2012-11-21
• Subjects: Algebra -- Periodicals; Algebra; Periodicals; Electronic journals; 512
• DOI: 10.5402/2012/170697
• Languages: English
• ISSNs: 2090-6285

Abstract

Abstract : The n th codimension c n ( 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 c n ( A ) as n goes to infinity. Since in most cases there is no hope in finding nice closed formula for c n ( A ), we study its asymptotics. We review here such results about c n ( A ), when A is an associative PI algebra. We start with the exponential bound on c n ( A ) then give few applications. We review some remarkable properties (integer and half integer) of the asymptotics of c n ( A ) . The representation theory of the symmetric group S n is an important tool in this theory.