{"title":"Minimal affine varieties of superalgebras with superinvolution: A characterization","authors":"Onofrio M. Di Vincenzo , Vincenzo C. Nardozza","doi":"10.1016/j.laa.2024.06.020","DOIUrl":null,"url":null,"abstract":"<div><p>We exhibit a class <span><math><mi>C</mi></math></span> of finite dimensional algebras with superinvolution over an algebraically closed field of characteristic zero, with the remarkable property that each member of <span><math><mi>C</mi></math></span> generates a minimal variety of algebras with superinvolution. This sums up to the fact that any affine minimal variety of algebras with superinvolution is generated by a suitable member of <span><math><mi>C</mi></math></span>, thus providing a complete characterization of the affine minimal varieties of algebras with superinvolution.</p></div>","PeriodicalId":18043,"journal":{"name":"Linear Algebra and its Applications","volume":null,"pages":null},"PeriodicalIF":1.0000,"publicationDate":"2024-06-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S002437952400274X/pdfft?md5=036a5bb31a29f608772f005e9a4e7256&pid=1-s2.0-S002437952400274X-main.pdf","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Linear Algebra and its Applications","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S002437952400274X","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
We exhibit a class of finite dimensional algebras with superinvolution over an algebraically closed field of characteristic zero, with the remarkable property that each member of generates a minimal variety of algebras with superinvolution. This sums up to the fact that any affine minimal variety of algebras with superinvolution is generated by a suitable member of , thus providing a complete characterization of the affine minimal varieties of algebras with superinvolution.
期刊介绍：
Linear Algebra and its Applications publishes articles that contribute new information or new insights to matrix theory and finite dimensional linear algebra in their algebraic, arithmetic, combinatorial, geometric, or numerical aspects. It also publishes articles that give significant applications of matrix theory or linear algebra to other branches of mathematics and to other sciences. Articles that provide new information or perspectives on the historical development of matrix theory and linear algebra are also welcome. Expository articles which can serve as an introduction to a subject for workers in related areas and which bring one to the frontiers of research are encouraged. Reviews of books are published occasionally as are conference reports that provide an historical record of major meetings on matrix theory and linear algebra.
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