6533b7cffe1ef96bd1258400

RESEARCH PRODUCT

Star-polynomial identities: computing the exponential growth of the codimensions

C. Polcino MiliesC. Polcino MiliesA. ValentiAntonio Giambruno

subject

Discrete mathematicsPure mathematicsAlgebra and Number Theory010102 general mathematicsSubalgebra010103 numerical & computational mathematicsBase field01 natural sciencesSuperalgebraExponential functionSettore MAT/02 - AlgebraExponential growthSuperinvolutionPolynomial identity Involution Superinvolution Codimensions0101 mathematicsAlgebraically closed fieldANÉIS E ÁLGEBRAS ASSOCIATIVOSMathematicsRate of growth

description

Abstract Can one compute the exponential rate of growth of the ⁎-codimensions of a PI-algebra with involution ⁎ over a field of characteristic zero? It was shown in [2] that any such algebra A has the same ⁎-identities as the Grassmann envelope of a finite dimensional superalgebra with superinvolution B. Here, by exploiting this result we are able to provide an exact estimate of the exponential rate of growth e x p ⁎ ( A ) of any PI-algebra A with involution. It turns out that e x p ⁎ ( A ) is an integer and, in case the base field is algebraically closed, it coincides with the dimension of an admissible subalgebra of maximal dimension of B.

yearjournalcountryeditionlanguage
2017-01-01
10.1016/j.jalgebra.2016.07.037