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arXiv · 2608.15612

Superalgebras and Algebras with Involution: Classifying Cubic Codimension Sequences

Yan-Hong Bao·Jiang-Nan Xu·Yuan-Feng Zhang
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Abstract

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.

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Yan-Hong Bao, Jiang-Nan Xu, Yuan-Feng Zhang. 2026-08-16. Superalgebras and Algebras with Involution: Classifying Cubic Codimension Sequences. https://arxiv.org/abs/2608.15612

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