Multialternating graded polynomials and growth of polynomial identities

Eli Aljadeff; Antonio Giambruno

doi:10.1090/S0002-9939-2013-11589-3

Multialternating graded polynomials and growth of polynomial identities

Eli Aljadeff, Antonio Giambruno

Research output: Contribution to journal › Article › peer-review

43 Scopus citations

Abstract

Let G be a finite group and A a finite dimensional G-graded algebra over a field of characteristic zero. When A is simple as a G-graded algebra, by means of Regev central polynomials we construct multialternating graded polynomials of arbitrarily large degree non-vanishing on A. As a consequence we compute the exponential rate of growth of the sequence of graded codi-mensions of an arbitrary G-graded algebra satisfying an ordinary polynomial identity. If c n (A),n = 1, 2,..., is the sequence of graded codimensions of A, we prove that exp (A) = lim_n-∞co ycn (A), the G-exponent of A, exists and is an integer. This result was proved by the authors and D. La Mattina in 2011 and by the second author and D. La Mattina in 2010 in the case G is abelian.

Original language	English
Pages (from-to)	3055-3065
Number of pages	11
Journal	Proceedings of the American Mathematical Society
Volume	141
Issue number	9
DOIs	https://doi.org/10.1090/S0002-9939-2013-11589-3
State	Published - 2013
Externally published	Yes

Keywords

Codimensions
Graded algebra
Growth
Polynomial identity

Access to Document

10.1090/S0002-9939-2013-11589-3

Cite this

@article{08f36209447f4b58b8567e3bd8ace2d8,

title = "Multialternating graded polynomials and growth of polynomial identities",

abstract = "Let G be a finite group and A a finite dimensional G-graded algebra over a field of characteristic zero. When A is simple as a G-graded algebra, by means of Regev central polynomials we construct multialternating graded polynomials of arbitrarily large degree non-vanishing on A. As a consequence we compute the exponential rate of growth of the sequence of graded codi-mensions of an arbitrary G-graded algebra satisfying an ordinary polynomial identity. If c n (A),n = 1, 2,..., is the sequence of graded codimensions of A, we prove that exp (A) = limn-∞co ycn (A), the G-exponent of A, exists and is an integer. This result was proved by the authors and D. La Mattina in 2011 and by the second author and D. La Mattina in 2010 in the case G is abelian.",

keywords = "Codimensions, Graded algebra, Growth, Polynomial identity",

author = "Eli Aljadeff and Antonio Giambruno",

year = "2013",

doi = "10.1090/S0002-9939-2013-11589-3",

language = "英语",

volume = "141",

pages = "3055--3065",

journal = "Proceedings of the American Mathematical Society",

issn = "0002-9939",

publisher = "American Mathematical Society",

number = "9",

}

TY - JOUR

T1 - Multialternating graded polynomials and growth of polynomial identities

AU - Aljadeff, Eli

AU - Giambruno, Antonio

PY - 2013

Y1 - 2013

N2 - Let G be a finite group and A a finite dimensional G-graded algebra over a field of characteristic zero. When A is simple as a G-graded algebra, by means of Regev central polynomials we construct multialternating graded polynomials of arbitrarily large degree non-vanishing on A. As a consequence we compute the exponential rate of growth of the sequence of graded codi-mensions of an arbitrary G-graded algebra satisfying an ordinary polynomial identity. If c n (A),n = 1, 2,..., is the sequence of graded codimensions of A, we prove that exp (A) = limn-∞co ycn (A), the G-exponent of A, exists and is an integer. This result was proved by the authors and D. La Mattina in 2011 and by the second author and D. La Mattina in 2010 in the case G is abelian.

AB - Let G be a finite group and A a finite dimensional G-graded algebra over a field of characteristic zero. When A is simple as a G-graded algebra, by means of Regev central polynomials we construct multialternating graded polynomials of arbitrarily large degree non-vanishing on A. As a consequence we compute the exponential rate of growth of the sequence of graded codi-mensions of an arbitrary G-graded algebra satisfying an ordinary polynomial identity. If c n (A),n = 1, 2,..., is the sequence of graded codimensions of A, we prove that exp (A) = limn-∞co ycn (A), the G-exponent of A, exists and is an integer. This result was proved by the authors and D. La Mattina in 2011 and by the second author and D. La Mattina in 2010 in the case G is abelian.

KW - Codimensions

KW - Graded algebra

KW - Growth

KW - Polynomial identity

UR - http://www.scopus.com/inward/record.url?scp=84879287957&partnerID=8YFLogxK

U2 - 10.1090/S0002-9939-2013-11589-3

DO - 10.1090/S0002-9939-2013-11589-3

M3 - 文章

AN - SCOPUS:84879287957

SN - 0002-9939

VL - 141

SP - 3055

EP - 3065

JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

IS - 9

ER -

Multialternating graded polynomials and growth of polynomial identities

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Cite this