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Abstract Let A be an associative algebra endowed with a superautomorphism φ . In this paper we completely classify the finite-dimensional simple algebras with superautomorphism of order ≤ 2. Moreover, after generalizing the Wedderburn–Malcev Theorem in this setting, we prove that the sequence of φ -codimensions of A is polynomially bounded if and only if the variety generated by A does not contain the group algebra of ℤ 2 and the algebra of 2 × 2 upper triangular matrices with suitable superautomorphisms.
Ioppolo et al. (Tue,) studied this question.