{"title":"Combinatorics of graded module categories over skew polynomial algebras at roots of unity","authors":"Akihiro Higashitani, Kenta Ueyama","doi":"arxiv-2409.10904","DOIUrl":null,"url":null,"abstract":"We introduce an operation on skew-symmetric matrices over\n$\\mathbb{Z}/\\ell\\mathbb{Z}$ called switching, and also define a class of\nskew-symmetric matrices over $\\mathbb{Z}/\\ell\\mathbb{Z}$ referred to as modular\nEulerian matrices. We then show that these are closely related to the graded\nmodule categories over skew polynomial algebras at $\\ell$-th roots of unity. As\nan application, we study the point simplicial complexes of skew polynomial\nalgebras at cube roots of unity.","PeriodicalId":501136,"journal":{"name":"arXiv - MATH - Rings and Algebras","volume":"196 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-09-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - MATH - Rings and Algebras","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2409.10904","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
We introduce an operation on skew-symmetric matrices over
$\mathbb{Z}/\ell\mathbb{Z}$ called switching, and also define a class of
skew-symmetric matrices over $\mathbb{Z}/\ell\mathbb{Z}$ referred to as modular
Eulerian matrices. We then show that these are closely related to the graded
module categories over skew polynomial algebras at $\ell$-th roots of unity. As
an application, we study the point simplicial complexes of skew polynomial
algebras at cube roots of unity.