2026/01/31 by Wesley Quaresma Cota, Luiz Henrique de Souza Matos
#math.RA
Let A be an associative algebra with a superinvolution * over a field of characteristic zero, and let cn^*(A), n = 1, 2, …, denote its sequence of *-codimensions. It is well known that this sequence is either polynomially bounded or grows exponentially. In the polynomial case, a central problem in PI-theory is the classification of varieties V for which cn^*(V) ≈ αnk for a given k. One of the main objectives of this paper is to classify minimal varieties of unitary algebras endowed with a superinvolution that exhibit quadratic codimension growth. We obtain a structural characterization, up to PI-equivalence, of all unitary algebras with quadratic codimension growth. As a consequence, we show that any unitary variety of quadratic codimension growth is generated by a direct sum of algebras generating minimal varieties.