{"title":"李色代数的混合张量不变量","authors":"Santosha Pattanayak, Preena Samuel","doi":"10.1016/j.laa.2025.01.003","DOIUrl":null,"url":null,"abstract":"<div><div>In this paper, we consider the mixed tensor space of a <em>G</em>-graded vector space, where <em>G</em> is a finite abelian group. We obtain a spanning set of invariants of the associated symmetric algebra under the action of a color analogue of the general linear group which we refer to as the general linear color group. As a consequence, we obtain a generating set for the polynomial invariants, under the simultaneous action of the general linear color group, on color analogues of several copies of matrices. We show that in this special case, this is the set of trace monomials, which coincides with the set of generators given by Berele in <span><span>[2]</span></span>.</div></div>","PeriodicalId":18043,"journal":{"name":"Linear Algebra and its Applications","volume":"709 ","pages":"Pages 1-17"},"PeriodicalIF":1.1000,"publicationDate":"2025-03-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Mixed tensor invariants of Lie color algebra\",\"authors\":\"Santosha Pattanayak, Preena Samuel\",\"doi\":\"10.1016/j.laa.2025.01.003\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><div>In this paper, we consider the mixed tensor space of a <em>G</em>-graded vector space, where <em>G</em> is a finite abelian group. We obtain a spanning set of invariants of the associated symmetric algebra under the action of a color analogue of the general linear group which we refer to as the general linear color group. As a consequence, we obtain a generating set for the polynomial invariants, under the simultaneous action of the general linear color group, on color analogues of several copies of matrices. We show that in this special case, this is the set of trace monomials, which coincides with the set of generators given by Berele in <span><span>[2]</span></span>.</div></div>\",\"PeriodicalId\":18043,\"journal\":{\"name\":\"Linear Algebra and its Applications\",\"volume\":\"709 \",\"pages\":\"Pages 1-17\"},\"PeriodicalIF\":1.1000,\"publicationDate\":\"2025-03-15\",\"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/S0024379525000047\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"2025/1/10 0:00:00\",\"PubModel\":\"Epub\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Linear Algebra and its Applications","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0024379525000047","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"2025/1/10 0:00:00","PubModel":"Epub","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
In this paper, we consider the mixed tensor space of a G-graded vector space, where G is a finite abelian group. We obtain a spanning set of invariants of the associated symmetric algebra under the action of a color analogue of the general linear group which we refer to as the general linear color group. As a consequence, we obtain a generating set for the polynomial invariants, under the simultaneous action of the general linear color group, on color analogues of several copies of matrices. We show that in this special case, this is the set of trace monomials, which coincides with the set of generators given by Berele in [2].
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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