Polynomial codimension growth of superalgebras with superautomorphism

In this paper we present some results concerning associative superalgebras endowed with a superautomorphism of order ≤2. We characterize the superalgebras with superautomorphism with multiplicities of the cocharacter bounded by a constant. Moreover, we determine the characterization of the superalgebras with superautomorphism with polynomial growth of the codimensions and we give a classification of the subvarieties of the varieties of almost polynomial growth. Finally, we characterize the superalgebras with superautomorphism with linear growth of the codimensions.