Superalgebras and Algebras with Involution: Classifying Cubic Codimension Sequences

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