6533b86efe1ef96bd12cbff6

RESEARCH PRODUCT

Central polynomials of graded algebras: Capturing their exponential growth

Daniela La MattinaFabrizio MartinoCarla Rizzo

subject

Settore MAT/02 - AlgebraAlgebra and Number TheoryCentral polynomialExponentCodimension growthPolynomial identity

description

Let G be a finite abelian group and let A be an associative G-graded algebra over a field of characteristic zero. A central G-polynomial is a polynomial of the free associative G-graded algebra that takes central values for all graded substitutions of homogeneous elements of A. We prove the existence and the integrability of two limits called the central G-exponent and the proper central G-exponent that give a quantitative measure of the growth of the central G-polynomials and the proper central G-polynomials, respectively. Moreover, we compare them with the G-exponent of the algebra.

yearjournalcountryeditionlanguage
2022-06-01
10.1016/j.jalgebra.2022.02.007http://hdl.handle.net/10447/538164