On superalgebras with pseudoautomorphism of polynomial codimension growth

Let A be an associative superalgebra endowed with a pseudoautomorphism p. In this paper we generalize the Wedderburn-Malcev Theorem in this setting and we prove that the sequence of p-codimensions of A is polynomially bounded if and only if the variety generated by A does not contain the group algebra of Z2 and the algebra of 2 × 2 upper-triangular matrices with suitable pseudoautomorphisms.