2024/12/23 by F. S. Benanti, Benanti, F. S., A. Valenti +1 · 1 citation
Mathematics · Computer Science · #Rings, Modules, and Algebras #Commutative Algebra and Its Applications #Polynomial and algebraic computation
paper · pdf · doi:10.48550/arxiv.2412.17689
Let F be a field of characteristic zero and let \mathcal V be a variety of associative F-algebras. In \citeregev2016 Regev introduced a numerical sequence measuring the growth of the proper central polynomials of a generating algebra of \mathcal V. Such sequence cnδ(\mathcal V), n ≥ 1, is called the sequence of proper central polynomials of \mathcal V and in \citeGZ2018, \citeGZ2019 the authors computed its exponential growth. This is an invariant of the variety. They also showed that cnδ(\mathcal V) either grows exponentially or is polynomially bounded. The purpose of this paper is to characterize the varieties of associative algebras whose exponential growth of cnδ(\mathcal V) is greater than two. As a consequence, we find a characterization of the varieties whose corresponding exponential growth is equal to two.