6533b853fe1ef96bd12ad52c

RESEARCH PRODUCT

Graded polynomial identities and codimensions: Computing the exponential growth

Antonio GiambrunoD. La Mattina

subject

Discrete mathematicsHilbert series and Hilbert polynomialPolynomialMathematics(all)Mathematics::Commutative AlgebraGeneral MathematicsGraded ringZero (complex analysis)GrowthPolynomial identityGraded algebraCodimensionssymbols.namesakepolynomial identity growthIntegerDifferential graded algebrasymbolsAbelian groupAlgebra over a fieldMathematics

description

Abstract Let G be a finite abelian group and A a G-graded algebra over a field of characteristic zero. This paper is devoted to a quantitative study of the graded polynomial identities satisfied by A. We study the asymptotic behavior of c n G ( A ) , n = 1 , 2 , … , the sequence of graded codimensions of A and we prove that if A satisfies an ordinary polynomial identity, lim n → ∞ c n G ( A ) n exists and is an integer. We give an explicit way of computing such integer by proving that it equals the dimension of a suitable finite dimension semisimple G × Z 2 -graded algebra related to A.

yearjournalcountryeditionlanguage
2010-10-01Advances in Mathematics
10.1016/j.aim.2010.03.013http://dx.doi.org/10.1016/j.aim.2010.03.013