{"title":"Standard monomials for temperley-lieb algebras","authors":"Sungsoon Kim, Dong-il Lee","doi":"10.1145/3055282.3055296","DOIUrl":null,"url":null,"abstract":"We deal with Temperley-Lieb algebras of type B, extending the result in [3, §6]. By completing the relations coming from a presentation of the Temperley-Lieb algebra, we find its Gröbner-Shirshov basis to obtain the corresponding set of standard monomials. The explicit multiplication table between the monomials follows naturally.","PeriodicalId":7093,"journal":{"name":"ACM Commun. Comput. Algebra","volume":"59 1","pages":"179-181"},"PeriodicalIF":0.0000,"publicationDate":"2017-02-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"ACM Commun. Comput. Algebra","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1145/3055282.3055296","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
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Abstract
We deal with Temperley-Lieb algebras of type B, extending the result in [3, §6]. By completing the relations coming from a presentation of the Temperley-Lieb algebra, we find its Gröbner-Shirshov basis to obtain the corresponding set of standard monomials. The explicit multiplication table between the monomials follows naturally.
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