2025/11/13 by Benanti, F. S., Valenti, A.
#FOS: Mathematics #Rings and Algebras (math.RA)
paper · doi:10.48550/arxiv.2511.10495
Let F be a field of characteristic zero and let \mathcal V^* be a variety of associative F-algebras with involution *. Associated to \mathcal V^* are three sequences: the sequence of \(*\)-codimensions \( c*n(\mathcal V^*) \), the sequence of central \(*\)-codimensions \( c*,zn(\mathcal V^*) \) and the sequence of proper central \(*\)-codimensions \( c*,δn(\mathcal V^*) \). These sequences provide information on the growth of, respectively, the *-polynomial identities, the central *-polynomial and the proper central *-polynomial of any generating algebra with involution A of \mathcal V^*. In \citeMR2022 it was proved that exp*,δ(\mathcal V^*)=limn→∞√[n]cn*,δ(\mathcal V^*) exists and is an integer called the proper central *-exponent. The aim of this paper is to study the varieties of associative algebras with involution of proper central *-exponent greater than two. To this end we construct a finite list of algebras with involution and we prove that if exp*,δ(\mathcal V^*) >2, then at least one of these algebras belongs to \mathcal V^*.