Polynomial codimension growth of algebras with involutions and superinvolutions

In this paper we focus our attention on such algebras since they are the only finite dimensional ⁎-algebras, up to T2⁎-equivalence, generating varieties of almost polynomial growth, i.e., varieties of exponential growth such that any proper subvariety has polynomial growth. We classify the subvarieties of such varieties by giving a complete list of generating finite dimensional ⁎-algebras. Along the way we classify all minimal varieties of polynomial growth and surprisingly we show that their number is finite for any given growth. Finally we describe the ⁎-algebras whose ⁎-codimensions are bounded by a linear function.