Fundamental superalgebras with superinvolution: exploiting minimal varieties

This paper extends the concept of fundamental superalgebra, crucial in Kemer’s resolution of the Specht problem, to the framework of superalgebras equipped with a superinvolution. We aim to characterize the class of these special algebras and provide concrete examples. Some of them are developed by exploring connections with varieties of superalgebras with superinvolution which are minimal with respect to their corresponding exponent.