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.
La Mattina, D., Martino, F., Rizzo, C. (2022). Central polynomials of graded algebras: Capturing their exponential growth. JOURNAL OF ALGEBRA, 600, 45-70 [10.1016/j.jalgebra.2022.02.007].
Central polynomials of graded algebras: Capturing their exponential growth
La Mattina, DanielaPrimo
;Martino, Fabrizio
Secondo
;
2022-01-01
Abstract
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.File | Dimensione | Formato | |
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