{"title":"so（3,1）到共轭的李子代数","authors":"R. Ghanam, G. Thompson, Narayana Bandara","doi":"10.1108/ajms-01-2022-0007","DOIUrl":null,"url":null,"abstract":"<jats:sec><jats:title content-type=\"abstract-subheading\">Purpose</jats:title><jats:p>This study aims to find all subalgebras up to conjugacy in the real simple Lie algebra <jats:inline-formula><m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"><m:mi mathvariant=\"fraktur\">s</m:mi><m:mi mathvariant=\"fraktur\">o</m:mi><m:mrow><m:mo>(</m:mo><m:mrow><m:mn>3,1</m:mn></m:mrow><m:mo>)</m:mo></m:mrow></m:math><jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"AJMS-01-2022-0007002.tif\" /></jats:inline-formula>.</jats:p></jats:sec><jats:sec><jats:title content-type=\"abstract-subheading\">Design/methodology/approach</jats:title><jats:p>The authors use Lie Algebra techniques to find all inequivalent subalgebras of <jats:inline-formula><m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"><m:mi mathvariant=\"fraktur\">s</m:mi><m:mi mathvariant=\"fraktur\">o</m:mi><m:mrow><m:mo>(</m:mo><m:mrow><m:mn>3,1</m:mn></m:mrow><m:mo>)</m:mo></m:mrow></m:math><jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"AJMS-01-2022-0007003.tif\" /></jats:inline-formula> in all dimensions.</jats:p></jats:sec><jats:sec><jats:title content-type=\"abstract-subheading\">Findings</jats:title><jats:p>The authors find all subalgebras up to conjugacy in the real simple Lie algebra <jats:inline-formula><m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"><m:mi mathvariant=\"fraktur\">s</m:mi><m:mi mathvariant=\"fraktur\">o</m:mi><m:mrow><m:mo>(</m:mo><m:mrow><m:mn>3,1</m:mn></m:mrow><m:mo>)</m:mo></m:mrow></m:math><jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"AJMS-01-2022-0007004.tif\" /></jats:inline-formula>.</jats:p></jats:sec><jats:sec><jats:title content-type=\"abstract-subheading\">Originality/value</jats:title><jats:p>This paper is an original research idea. It will be a main reference for many applications such as solving partial differential equations. If <jats:inline-formula><m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"><m:mi mathvariant=\"fraktur\">s</m:mi><m:mi mathvariant=\"fraktur\">o</m:mi><m:mrow><m:mo>(</m:mo><m:mrow><m:mn>3,1</m:mn></m:mrow><m:mo>)</m:mo></m:mrow></m:math><jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"AJMS-01-2022-0007005.tif\" /></jats:inline-formula> is part of the symmetry Lie algebra, then the subalgebras listed in this paper will be used to reduce the order of the partial differential equation (PDE) and produce non-equivalent solutions.</jats:p></jats:sec>","PeriodicalId":36840,"journal":{"name":"Arab Journal of Mathematical Sciences","volume":" ","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2022-06-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","resultStr":"{\"title\":\"Lie subalgebras of so(3,1) up to conjugacy\",\"authors\":\"R. Ghanam, G. Thompson, Narayana Bandara\",\"doi\":\"10.1108/ajms-01-2022-0007\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<jats:sec><jats:title content-type=\\\"abstract-subheading\\\">Purpose</jats:title><jats:p>This study aims to find all subalgebras up to conjugacy in the real simple Lie algebra <jats:inline-formula><m:math xmlns:m=\\\"http://www.w3.org/1998/Math/MathML\\\"><m:mi mathvariant=\\\"fraktur\\\">s</m:mi><m:mi mathvariant=\\\"fraktur\\\">o</m:mi><m:mrow><m:mo>(</m:mo><m:mrow><m:mn>3,1</m:mn></m:mrow><m:mo>)</m:mo></m:mrow></m:math><jats:inline-graphic xmlns:xlink=\\\"http://www.w3.org/1999/xlink\\\" xlink:href=\\\"AJMS-01-2022-0007002.tif\\\" /></jats:inline-formula>.</jats:p></jats:sec><jats:sec><jats:title content-type=\\\"abstract-subheading\\\">Design/methodology/approach</jats:title><jats:p>The authors use Lie Algebra techniques to find all inequivalent subalgebras of <jats:inline-formula><m:math xmlns:m=\\\"http://www.w3.org/1998/Math/MathML\\\"><m:mi mathvariant=\\\"fraktur\\\">s</m:mi><m:mi mathvariant=\\\"fraktur\\\">o</m:mi><m:mrow><m:mo>(</m:mo><m:mrow><m:mn>3,1</m:mn></m:mrow><m:mo>)</m:mo></m:mrow></m:math><jats:inline-graphic xmlns:xlink=\\\"http://www.w3.org/1999/xlink\\\" xlink:href=\\\"AJMS-01-2022-0007003.tif\\\" /></jats:inline-formula> in all dimensions.</jats:p></jats:sec><jats:sec><jats:title content-type=\\\"abstract-subheading\\\">Findings</jats:title><jats:p>The authors find all subalgebras up to conjugacy in the real simple Lie algebra <jats:inline-formula><m:math xmlns:m=\\\"http://www.w3.org/1998/Math/MathML\\\"><m:mi mathvariant=\\\"fraktur\\\">s</m:mi><m:mi mathvariant=\\\"fraktur\\\">o</m:mi><m:mrow><m:mo>(</m:mo><m:mrow><m:mn>3,1</m:mn></m:mrow><m:mo>)</m:mo></m:mrow></m:math><jats:inline-graphic xmlns:xlink=\\\"http://www.w3.org/1999/xlink\\\" xlink:href=\\\"AJMS-01-2022-0007004.tif\\\" /></jats:inline-formula>.</jats:p></jats:sec><jats:sec><jats:title content-type=\\\"abstract-subheading\\\">Originality/value</jats:title><jats:p>This paper is an original research idea. It will be a main reference for many applications such as solving partial differential equations. If <jats:inline-formula><m:math xmlns:m=\\\"http://www.w3.org/1998/Math/MathML\\\"><m:mi mathvariant=\\\"fraktur\\\">s</m:mi><m:mi mathvariant=\\\"fraktur\\\">o</m:mi><m:mrow><m:mo>(</m:mo><m:mrow><m:mn>3,1</m:mn></m:mrow><m:mo>)</m:mo></m:mrow></m:math><jats:inline-graphic xmlns:xlink=\\\"http://www.w3.org/1999/xlink\\\" xlink:href=\\\"AJMS-01-2022-0007005.tif\\\" /></jats:inline-formula> is part of the symmetry Lie algebra, then the subalgebras listed in this paper will be used to reduce the order of the partial differential equation (PDE) and produce non-equivalent solutions.</jats:p></jats:sec>\",\"PeriodicalId\":36840,\"journal\":{\"name\":\"Arab Journal of Mathematical Sciences\",\"volume\":\" \",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2022-06-02\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"2\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Arab Journal of Mathematical Sciences\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1108/ajms-01-2022-0007\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"Mathematics\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Arab Journal of Mathematical Sciences","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1108/ajms-01-2022-0007","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"Mathematics","Score":null,"Total":0}
PurposeThis study aims to find all subalgebras up to conjugacy in the real simple Lie algebra so(3,1).Design/methodology/approachThe authors use Lie Algebra techniques to find all inequivalent subalgebras of so(3,1) in all dimensions.FindingsThe authors find all subalgebras up to conjugacy in the real simple Lie algebra so(3,1).Originality/valueThis paper is an original research idea. It will be a main reference for many applications such as solving partial differential equations. If so(3,1) is part of the symmetry Lie algebra, then the subalgebras listed in this paper will be used to reduce the order of the partial differential equation (PDE) and produce non-equivalent solutions.
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