{"title":"Tied–boxed algebras","authors":"Diego Arcis , Jorge Espinoza","doi":"10.1016/j.jalgebra.2025.07.039","DOIUrl":null,"url":null,"abstract":"<div><div>We introduce two new algebras that we call <em>tied–boxed Hecke algebra</em> and <em>tied–boxed Temperley–Lieb algebra</em>. The first one is a subalgebra of the algebra of braids and ties introduced by Aicardi and Juyumaya, and the second one is a tied-version of the well known Temperley–Lieb algebra. We study their representation theory and give cellular bases for them. Furthermore, we explore a strong connection between the tied–boxed Temperley–Lieb algebra and the so-called partition Temperley–Lieb algebra given by Juyumaya. Also, we show that both structures inherit diagrammatic interpretations from a new class of monoids that we call <em>boxed ramified monoids</em>. Additionally, we give presentations for the singular part of the ramified symmetric monoid and for the boxed ramified monoid associated to the Brauer monoid.</div></div>","PeriodicalId":14888,"journal":{"name":"Journal of Algebra","volume":"685 ","pages":"Pages 112-159"},"PeriodicalIF":0.8000,"publicationDate":"2025-08-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Algebra","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0021869325004545","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
We introduce two new algebras that we call tied–boxed Hecke algebra and tied–boxed Temperley–Lieb algebra. The first one is a subalgebra of the algebra of braids and ties introduced by Aicardi and Juyumaya, and the second one is a tied-version of the well known Temperley–Lieb algebra. We study their representation theory and give cellular bases for them. Furthermore, we explore a strong connection between the tied–boxed Temperley–Lieb algebra and the so-called partition Temperley–Lieb algebra given by Juyumaya. Also, we show that both structures inherit diagrammatic interpretations from a new class of monoids that we call boxed ramified monoids. Additionally, we give presentations for the singular part of the ramified symmetric monoid and for the boxed ramified monoid associated to the Brauer monoid.
期刊介绍:
The Journal of Algebra is a leading international journal and publishes papers that demonstrate high quality research results in algebra and related computational aspects. Only the very best and most interesting papers are to be considered for publication in the journal. With this in mind, it is important that the contribution offer a substantial result that will have a lasting effect upon the field. The journal also seeks work that presents innovative techniques that offer promising results for future research.