{"title":"On the asymptotic behaviour of the graded-star-codimension sequence of upper triangular matrices","authors":"Diogo Diniz, Felipe Yukihide Yasumura","doi":"arxiv-2408.00087","DOIUrl":null,"url":null,"abstract":"We study the algebra of upper triangular matrices endowed with a group\ngrading and a homogeneous involution over an infinite field. We compute the\nasymptotic behaviour of its (graded) star-codimension sequence. It turns out\nthat the asymptotic growth of the sequence is independent of the grading and\nthe involution under consideration, depending solely on the size of the matrix\nalgebra. This independence of the group grading also applies to the graded\ncodimension sequence of the associative algebra of upper triangular matrices.","PeriodicalId":501136,"journal":{"name":"arXiv - MATH - Rings and Algebras","volume":"44 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-07-31","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-2408.00087","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 study the algebra of upper triangular matrices endowed with a group
grading and a homogeneous involution over an infinite field. We compute the
asymptotic behaviour of its (graded) star-codimension sequence. It turns out
that the asymptotic growth of the sequence is independent of the grading and
the involution under consideration, depending solely on the size of the matrix
algebra. This independence of the group grading also applies to the graded
codimension sequence of the associative algebra of upper triangular matrices.