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PreprintCC BY 4.0arXiv

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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Cite

BibTeXRIS
BibTeX
@misc{cota2026varieties,
  title = {{Varieties of associative algebras with quadratic codimension growth}},
  author = {Wesley Quaresma Cota and Luiz Henrique de Souza Matos and Pedro Quintino},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2608.22966},
  eprint = {2608.22966},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2608.22966},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Varieties of associative algebras with quadratic codimension growth
AU  - Wesley Quaresma Cota
AU  - Luiz Henrique de Souza Matos
AU  - Pedro Quintino
PY  - 2026
DA  - 2026/09/14
PB  - arXiv
DO  - 10.48550/arxiv.2608.22966
UR  - https://arxiv.org/abs/2608.22966
AB  - 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.
ER  -