Scholarlink

<p><?tk 2?>Numerical invariant sequences associated with algebras have gained increasing attention due to their role in understanding the asymptotic behavior of polynomial identities. This work aims to provide a comprehensive overview of results concerning the colength sequence in many settings of PI-algebras, particularly algebras with involution, graded algebras and algebras with graded involution or superinvolution. We begin by recalling the fundamental definitions and motivations behind the study of colength, emphasizing its connection with codimension growth and other properties of PI-algebras. Finally, we present the main results recently obtained about the colength sequence of algebras with additional structures.</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

Classification of varieties with bounded colength: a view through recent advances

  • 期刊论文

  • 出版模式：

    开放获取

  • 发表日期：

    2026年3月25日

查看全文
  • Wesley Quaresma Cota,
  • Thais Silva do Nascimento,
  • Ana Cristina Vieira

摘要

Numerical invariant sequences associated with algebras have gained increasing attention due to their role in understanding the asymptotic behavior of polynomial identities. This work aims to provide a comprehensive overview of results concerning the colength sequence in many settings of PI-algebras, particularly algebras with involution, graded algebras and algebras with graded involution or superinvolution. We begin by recalling the fundamental definitions and motivations behind the study of colength, emphasizing its connection with codimension growth and other properties of PI-algebras. Finally, we present the main results recently obtained about the colength sequence of algebras with additional structures.