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

2025/04/27 by Yanan Bao, Dong‐Jing Fu, Bao, Y. -H. +11
Mathematics · #Advanced Topics in Algebra #Commutative Algebra and Its Applications #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Rings and Algebras (math.RA)

paper · pdf · doi:10.48550/arxiv.2504.19168

openalex publication_date 2025/04/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 ≤ 6. This corresponds to a classification of all T-ideals of codimension growth n^g with g≤ 5 (or equivalently, varieties of grade g with g≤ 5).

Citations

• Ideals of the associative algebra operad
• Gerstenhaber and Batalin-Vilkovisky structures on modules over operads
• Algebraic Properties of Codimension Series of PI-Algebras
• Batalin-Vilkovisky algebras and cyclic cohomology of Hopf algebras

Related

• Ideals of the associative algebra operad
• Group graded algebras and varieties with quadratic codimension growth
• A structural classification of algebras with graded involution and quadratic codimension growth
• Higher dimensional operads
• Operads with trivial \mathbbA-actions