{"title":"Gradings on associative triple systems of the second kind","authors":"Alberto Daza-Garcia","doi":"10.1016/j.laa.2024.07.015","DOIUrl":null,"url":null,"abstract":"<div><div>On this work we study associative triple systems of the second kind. We show that for simple triple systems the automorphism group scheme is isomorphic to the automorphism group scheme of the 3-graded associative algebra with involution constructed by Loos. This result will allow us to prove our main result which is a complete classification up to isomorphism of the gradings of structurable algebras.</div></div>","PeriodicalId":18043,"journal":{"name":"Linear Algebra and its Applications","volume":null,"pages":null},"PeriodicalIF":1.0000,"publicationDate":"2024-07-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Linear Algebra and its Applications","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0024379524003057","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
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Abstract
On this work we study associative triple systems of the second kind. We show that for simple triple systems the automorphism group scheme is isomorphic to the automorphism group scheme of the 3-graded associative algebra with involution constructed by Loos. This result will allow us to prove our main result which is a complete classification up to isomorphism of the gradings of structurable algebras.
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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