{"title":"A Note on the Quantum Berezinian for the Double Yangian of the Lie Superalgebra \\(\\mathfrak {gl}_{m|n}\\)","authors":"Lucia Bagnoli, Slaven Kožić","doi":"10.1007/s10468-024-10310-9","DOIUrl":null,"url":null,"abstract":"<div><p>In this note, we generalize the notion of quantum Berezinian to the double Yangian <span>\\(\\textrm{DY}(\\mathfrak {gl}_{m|n})\\)</span> of the Lie superalgebra <span>\\( \\mathfrak {gl}_{m|n} \\)</span>. We show that its coefficients form a family of algebraically independent topological generators of the center of <span>\\(\\textrm{DY}(\\mathfrak {gl}_{m|n})\\)</span>.</p></div>","PeriodicalId":50825,"journal":{"name":"Algebras and Representation Theory","volume":"28 1","pages":"143 - 155"},"PeriodicalIF":0.6000,"publicationDate":"2024-12-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Algebras and Representation Theory","FirstCategoryId":"100","ListUrlMain":"https://link.springer.com/article/10.1007/s10468-024-10310-9","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
In this note, we generalize the notion of quantum Berezinian to the double Yangian \(\textrm{DY}(\mathfrak {gl}_{m|n})\) of the Lie superalgebra \( \mathfrak {gl}_{m|n} \). We show that its coefficients form a family of algebraically independent topological generators of the center of \(\textrm{DY}(\mathfrak {gl}_{m|n})\).
期刊介绍：
Algebras and Representation Theory features carefully refereed papers relating, in its broadest sense, to the structure and representation theory of algebras, including Lie algebras and superalgebras, rings of differential operators, group rings and algebras, C*-algebras and Hopf algebras, with particular emphasis on quantum groups.
The journal contains high level, significant and original research papers, as well as expository survey papers written by specialists who present the state-of-the-art of well-defined subjects or subdomains. Occasionally, special issues on specific subjects are published as well, the latter allowing specialists and non-specialists to quickly get acquainted with new developments and topics within the field of rings, algebras and their applications.
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