{"title":"由自同构诱导的广义中心对称矩阵代数","authors":"Huabo Xu","doi":"10.1142/s1005386722000426","DOIUrl":null,"url":null,"abstract":"Let [Formula: see text] be a ring with an automorphism [Formula: see text] of order two. We introduce the definition of [Formula: see text]-centrosymmetric matrices. Denote by [Formula: see text] the ring of all [Formula: see text] matrices over [Formula: see text], and by [Formula: see text] the set of all [Formula: see text]-centrosymmetric [Formula: see text] matrices over [Formula: see text] for any positive integer [Formula: see text]. We show that [Formula: see text] is a separable Frobenius extension. If [Formula: see text] is commutative, then [Formula: see text] is a cellular algebra over the invariant subring [Formula: see text] of [Formula: see text].","PeriodicalId":50958,"journal":{"name":"Algebra Colloquium","volume":"73 2","pages":""},"PeriodicalIF":0.4000,"publicationDate":"2022-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Generalized Centrosymmetric Matrix Algebras Induced by Automorphisms\",\"authors\":\"Huabo Xu\",\"doi\":\"10.1142/s1005386722000426\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Let [Formula: see text] be a ring with an automorphism [Formula: see text] of order two. We introduce the definition of [Formula: see text]-centrosymmetric matrices. Denote by [Formula: see text] the ring of all [Formula: see text] matrices over [Formula: see text], and by [Formula: see text] the set of all [Formula: see text]-centrosymmetric [Formula: see text] matrices over [Formula: see text] for any positive integer [Formula: see text]. We show that [Formula: see text] is a separable Frobenius extension. If [Formula: see text] is commutative, then [Formula: see text] is a cellular algebra over the invariant subring [Formula: see text] of [Formula: see text].\",\"PeriodicalId\":50958,\"journal\":{\"name\":\"Algebra Colloquium\",\"volume\":\"73 2\",\"pages\":\"\"},\"PeriodicalIF\":0.4000,\"publicationDate\":\"2022-12-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Algebra Colloquium\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1142/s1005386722000426\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Algebra Colloquium","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1142/s1005386722000426","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS","Score":null,"Total":0}
Generalized Centrosymmetric Matrix Algebras Induced by Automorphisms
Let [Formula: see text] be a ring with an automorphism [Formula: see text] of order two. We introduce the definition of [Formula: see text]-centrosymmetric matrices. Denote by [Formula: see text] the ring of all [Formula: see text] matrices over [Formula: see text], and by [Formula: see text] the set of all [Formula: see text]-centrosymmetric [Formula: see text] matrices over [Formula: see text] for any positive integer [Formula: see text]. We show that [Formula: see text] is a separable Frobenius extension. If [Formula: see text] is commutative, then [Formula: see text] is a cellular algebra over the invariant subring [Formula: see text] of [Formula: see text].
期刊介绍：
Algebra Colloquium is an international mathematical journal founded at the beginning of 1994. It is edited by the Academy of Mathematics & Systems Science, Chinese Academy of Sciences, jointly with Suzhou University, and published quarterly in English in every March, June, September and December. Algebra Colloquium carries original research articles of high level in the field of pure and applied algebra. Papers from related areas which have applications to algebra are also considered for publication. This journal aims to reflect the latest developments in algebra and promote international academic exchanges.
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