{"title":"On Integrality of Non-Semisimple Quantum Representations of Mapping Class Groups","authors":"Marco De Renzi, Jules Martel","doi":"arxiv-2407.20644","DOIUrl":null,"url":null,"abstract":"For a root of unity $\\zeta$ of odd prime order, we restrict coefficients of\nnon-semisimple quantum representations of mapping class groups associated with\nthe small quantum group $\\mathfrak{u}_\\zeta \\mathfrak{sl}_2$ from\n$\\mathbb{Q}(\\zeta)$ to $\\mathbb{Z}[\\zeta]$. We do this by exhibiting explicit\nbases of states spaces that span $\\mathbb{Z}[\\zeta]$-lattices that are\ninvariant under projective actions of mapping class groups.","PeriodicalId":501317,"journal":{"name":"arXiv - MATH - Quantum Algebra","volume":"161 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-07-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - MATH - Quantum Algebra","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2407.20644","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
For a root of unity $\zeta$ of odd prime order, we restrict coefficients of
non-semisimple quantum representations of mapping class groups associated with
the small quantum group $\mathfrak{u}_\zeta \mathfrak{sl}_2$ from
$\mathbb{Q}(\zeta)$ to $\mathbb{Z}[\zeta]$. We do this by exhibiting explicit
bases of states spaces that span $\mathbb{Z}[\zeta]$-lattices that are
invariant under projective actions of mapping class groups.