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Growth for Algebras Satisfying Polynomial Identities
Author
Source
Issue
Vol. 2012, Issue 2012 (31 Dec. 2012), pp.1-26, 26 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2012-11-21
Country of Publication
Egypt
No. of Pages
26
Main Subjects
Abstract 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.
American Psychological Association (APA)
Regev, Amitai. 2012. Growth for Algebras Satisfying Polynomial Identities. ISRN Algebra،Vol. 2012, no. 2012, pp.1-26.
https://search.emarefa.net/detail/BIM-451510
Modern Language Association (MLA)
Regev, Amitai. Growth for Algebras Satisfying Polynomial Identities. ISRN Algebra No. 2012 (2012), pp.1-26.
https://search.emarefa.net/detail/BIM-451510
American Medical Association (AMA)
Regev, Amitai. Growth for Algebras Satisfying Polynomial Identities. ISRN Algebra. 2012. Vol. 2012, no. 2012, pp.1-26.
https://search.emarefa.net/detail/BIM-451510
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-451510