On the identities and cocharacters of the algebra of $3 \times 3$ matrices with orthosymplectic superinvolution

Sara Accomando
{"title":"On the identities and cocharacters of the algebra of $3 \\times 3$ matrices with orthosymplectic superinvolution","authors":"Sara Accomando","doi":"arxiv-2409.10187","DOIUrl":null,"url":null,"abstract":"Let $M_{1,2}(F)$ be the algebra of $3 \\times 3$ matrices with orthosymplectic\nsuperinvolution $*$ over a field $F$ of characteristic zero. We study the\n$*$-identities of this algebra through the representation theory of the group\n$\\mathbb{H}_n = (\\mathbb{Z}_2 \\times \\mathbb{Z}_2) \\sim S_n$. We decompose the\nspace of multilinear $*$-identities of degree $n$ into the sum of irreducibles\nunder the $\\mathbb{H}_n$-action in order to study the irreducible characters\nappearing in this decomposition with non-zero multiplicity. Moreover, by using\nthe representation theory of the general linear group, we determine all the\n$*$-polynomial identities of $M_{1,2}(F)$ up to degree $3$.","PeriodicalId":501136,"journal":{"name":"arXiv - MATH - Rings and Algebras","volume":"51 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-09-16","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-2409.10187","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

Let $M_{1,2}(F)$ be the algebra of $3 \times 3$ matrices with orthosymplectic superinvolution $*$ over a field $F$ of characteristic zero. We study the $*$-identities of this algebra through the representation theory of the group $\mathbb{H}_n = (\mathbb{Z}_2 \times \mathbb{Z}_2) \sim S_n$. We decompose the space of multilinear $*$-identities of degree $n$ into the sum of irreducibles under the $\mathbb{H}_n$-action in order to study the irreducible characters appearing in this decomposition with non-zero multiplicity. Moreover, by using the representation theory of the general linear group, we determine all the $*$-polynomial identities of $M_{1,2}(F)$ up to degree $3$.
查看原文
分享 分享
微信好友 朋友圈 QQ好友 复制链接
本刊更多论文
论具有正交超卷积的 3 美元乘 3 美元矩阵代数的同调与共调
让 $M_{1,2}(F)$ 是在特征为零的域 $F$ 上具有正交超卷积 $*$ 的 3 \times 3$ 矩阵的代数。我们通过组$mathbb{H}_n = (\mathbb{Z}_2 \times \mathbb{Z}_2) \sim S_n$ 的表示理论来研究这个代数的$*$-同一性。我们将阶数为 $n$ 的多线性 $*$-identity 空间分解为 $\mathbb{H}_n$ 作用下的不可约数之和,以研究在此分解中出现的具有非零多重性的不可约数特征。此外,通过使用一般线性群的表示理论,我们确定了$M_{1,2}(F)$直到3$度的所有$*$-polynomial 特性。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
求助全文
约1分钟内获得全文 去求助
来源期刊
自引率
0.00%
发文量
0
期刊最新文献
New characterization of $(b,c)$-inverses through polarity Relative torsionfreeness and Frobenius extensions Signature matrices of membranes On denominator conjecture for cluster algebras of finite type Noetherianity of Diagram Algebras
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
×
提示
您的信息不完整,为了账户安全,请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
现在去查看 取消
×
提示
确定
0
微信
客服QQ
Book学术公众号 扫码关注我们
反馈
×
意见反馈
请填写您的意见或建议
请填写您的手机或邮箱
已复制链接
已复制链接
快去分享给好友吧!
我知道了
×
扫码分享
扫码分享
Book学术官方微信
Book学术文献互助
Book学术文献互助群
群 号:481959085
Book学术
文献互助 智能选刊 最新文献 互助须知 联系我们:info@booksci.cn
Book学术提供免费学术资源搜索服务,方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。
Copyright © 2023 Book学术 All rights reserved.
ghs 京公网安备 11010802042870号 京ICP备2023020795号-1