Codimension sequence, grade, and generating degree: an operadic approach

Y. -H. Bao; D. -X. Fu; J. -N. Xu; Y. Ye; J. J. Zhang; Y. -F. Zhang; Z. -B. Zhao

Codimension sequence, grade, and generating degree: an operadic approach

Rings and Algebras 2025-08-06 v4

Authors: Y. -H. Bao , D. -X. Fu , J. -N. Xu , Y. Ye , J. J. Zhang , Y. -F. Zhang , Z. -B. Zhao

Abstract

We study several classes of operadic ideals of the unital associative algebra operad $\uas$ . As an application, we classify quotient operads of $\uas$ of GK-dimension $\leq 6$ . This corresponds to a classification of all T-ideals of codimension growth $n^g$ with $g\leq 5$ (or equivalently, varieties of grade $g$ with $g\leq 5$ ).

Keywords

operad theory graded algebras

Cite

@article{arxiv.2504.19168,
  title  = {Codimension sequence, grade, and generating degree: an operadic approach},
  author = {Y. -H. Bao and D. -X. Fu and J. -N. Xu and Y. Ye and J. J. Zhang and Y. -F. Zhang and Z. -B. Zhao},
  journal= {arXiv preprint arXiv:2504.19168},
  year   = {2025}
}

Codimension sequence, grade, and generating degree: an operadic approach

Abstract

Keywords

Cite

Related papers