On minimal varieties of superalgebras with superautomorphism

Let A be a finite-dimensional superalgebra with superautomorphism ϕ over a field of characteristic zero. In [11] the authors gave a positive answer to the Amitsur’s conjecture in this setting showing that the ϕ-exponent of A exists and it is an integer. In the present paper we extend the notion of minimal variety to the context of superalgebras with superautomorphism and prove that a variety is minimal of fixed ϕ-exponent if, and only if, it is generated by a subalgebra of an upper block triangular matrix algebra equipped with a suitable elementary Z2-grading and superautomorphism. Along the way, we give a contribution on the isomorphism question within the theory of polynomial identities