On the central exponent of superalgebras with superinvolution

The growth of central polynomials for matrix algebras over a field of characteristic zero was first studied by Regev in 2016. This problem can be generalized by analyzing the behavior of the dimension czn(A) of the space of multilinear polynomials of degree n modulo the central polynomials of an algebra A. In 2018, Giambruno and Zaicev established the existence of the limit limn→∞n √ czn(A). In this paper, we extend this framework to superalgebras equipped with a superinvolution, proving both the existence and the finiteness of the corresponding limit.