6533b821fe1ef96bd127c229

RESEARCH PRODUCT

Multialternating graded polynomials and growth of polynomial identities

Antonio GiambrunoEli Aljadeff

subject

Discrete mathematicsPure mathematicsHilbert series and Hilbert polynomialMathematics::Commutative AlgebraApplied MathematicsGeneral MathematicsMathematics::Rings and AlgebrasGraded ringMathematics - Rings and AlgebrasGraded Lie algebramultialternating polynomialFiltered algebrasymbols.namesakeReciprocal polynomialRings and Algebras (math.RA)Differential graded algebraFactorization of polynomialssymbolsFOS: MathematicsElementary symmetric polynomial16R50 16P90 16R10 16W50Mathematics

description

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 mean 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 codimensions of an arbitrary G-graded algebra satisfying an ordinary polynomial identity. In particular we show it is an integer. The result was proviously known in case G is abelian.

yearjournalcountryeditionlanguage
2012-04-14
https://dx.doi.org/10.48550/arxiv.1204.3159