Superalgebras and Algebras with Involution: Classifying Cubic Codimension Sequences

Abstract

A $φ$-algebra is either a superalgebra or an algebra with involution. In this paper, we study $\operatorname{T}^φ$-ideals associated with unital $φ$-algebras whose $φ$-codimension sequence exhibits cubic polynomial growth. As a consequence, we obtain a complete classification of all $φ$-codimension sequences of cubic growth for unital $φ$-algebras. Furthermore, we explicitly determine a minimal-degree multilinear generator for every $\operatorname{T}^φ$-ideal associated with unital $φ$-algebras whose $φ$-codimension growth is at most quadratic.