Abstract
Let A be an associative algebra with superinvolution ∗ over a field of characteristic zero and let \(c_{n}^{\ast }(A)\) be its sequence of corresponding ∗-codimensions. In case A is finite dimensional, we prove that such sequence is polynomially bounded if and only if the variety generated by A does not contain three explicitly described algebras with superinvolution. As a consequence we find out that no intermediate growth of the ∗-codimensions between polynomial and exponential is allowed.
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