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arXiv · 2608.22966

Varieties of associative algebras with quadratic codimension growth

Wesley Quaresma Cota·Luiz Henrique de Souza Matos·Pedro Quintino
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Abstract

We classify, up to PI-equivalence, associative algebras over a field of characteristic zero whose codimension sequences have quadratic growth. More precisely, making use of fundamental algebras, we prove that every such algebra is PI-equivalent to a finite direct sum of algebras generating minimal varieties of at most quadratic codimension growth, together with a possible nilpotent summand.

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Wesley Quaresma Cota, Luiz Henrique de Souza Matos, Pedro Quintino. 2026-09-14. Varieties of associative algebras with quadratic codimension growth. https://arxiv.org/abs/2608.22966

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