{"title":"Minimal varieties of PI-algebras with graded involution","authors":"F.S. Benanti , O.M. Di Vincenzo , A. Valenti","doi":"10.1016/j.laa.2024.07.010","DOIUrl":null,"url":null,"abstract":"<div><p>Let F be an algebraically closed field of characteristic zero and <em>G</em> a cyclic group of odd prime order. We consider the class of finite dimensional <span><math><mo>(</mo><mi>G</mi><mo>,</mo><mo>⁎</mo><mo>)</mo></math></span>-algebras, namely <em>G</em>-graded algebras endowed with graded involution ⁎, and we characterize the varieties generated by algebras of this class which are minimal with respect to the <span><math><mo>(</mo><mi>G</mi><mo>,</mo><mo>⁎</mo><mo>)</mo></math></span>-exponent.</p></div>","PeriodicalId":18043,"journal":{"name":"Linear Algebra and its Applications","volume":null,"pages":null},"PeriodicalIF":1.0000,"publicationDate":"2024-07-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0024379524003008/pdfft?md5=58c6ef0e78e02e4ca980c259967a3439&pid=1-s2.0-S0024379524003008-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/S0024379524003008","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
Let F be an algebraically closed field of characteristic zero and G a cyclic group of odd prime order. We consider the class of finite dimensional -algebras, namely G-graded algebras endowed with graded involution ⁎, and we characterize the varieties generated by algebras of this class which are minimal with respect to the -exponent.
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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