{"title":"模型丝状列超拉的局部自动和局部超分化","authors":"Yuqiu Sheng, Wende Liu, Yang Liu","doi":"10.1155/2024/6650997","DOIUrl":null,"url":null,"abstract":"In this paper, we give the forms of local automorphisms (resp. superderivations) of model filiform Lie superalgebra <svg height=\"12.9866pt\" style=\"vertical-align:-4.3507pt\" version=\"1.1\" viewbox=\"-0.0498162 -8.6359 23.1172 12.9866\" width=\"23.1172pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"><g transform=\"matrix(.013,0,0,-0.013,0,0)\"></path></g><g transform=\"matrix(.0091,0,0,-0.0091,8.294,3.132)\"></path></g><g transform=\"matrix(.0091,0,0,-0.0091,12.953,3.132)\"></path></g><g transform=\"matrix(.0091,0,0,-0.0091,15.11,3.132)\"></path></g></svg> in the matrix version. Linear 2-local automorphisms (resp. superderivations) of <svg height=\"12.9866pt\" style=\"vertical-align:-4.3507pt\" version=\"1.1\" viewbox=\"-0.0498162 -8.6359 23.1172 12.9866\" width=\"23.1172pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"><g transform=\"matrix(.013,0,0,-0.013,0,0)\"><use xlink:href=\"#g113-77\"></use></g><g transform=\"matrix(.0091,0,0,-0.0091,8.294,3.132)\"><use xlink:href=\"#g50-111\"></use></g><g transform=\"matrix(.0091,0,0,-0.0091,12.953,3.132)\"><use xlink:href=\"#g50-45\"></use></g><g transform=\"matrix(.0091,0,0,-0.0091,15.11,3.132)\"><use xlink:href=\"#g50-110\"></use></g></svg> are also characterized. We prove that each linear 2-local automorphism of <svg height=\"12.9866pt\" style=\"vertical-align:-4.3507pt\" version=\"1.1\" viewbox=\"-0.0498162 -8.6359 23.1172 12.9866\" width=\"23.1172pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"><g transform=\"matrix(.013,0,0,-0.013,0,0)\"><use xlink:href=\"#g113-77\"></use></g><g transform=\"matrix(.0091,0,0,-0.0091,8.294,3.132)\"><use xlink:href=\"#g50-111\"></use></g><g transform=\"matrix(.0091,0,0,-0.0091,12.953,3.132)\"><use xlink:href=\"#g50-45\"></use></g><g transform=\"matrix(.0091,0,0,-0.0091,15.11,3.132)\"><use xlink:href=\"#g50-110\"></use></g></svg> is an automorphism.","PeriodicalId":54214,"journal":{"name":"Journal of Mathematics","volume":"9 1","pages":""},"PeriodicalIF":1.3000,"publicationDate":"2024-03-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Local Automorphisms and Local Superderivations of Model Filiform Lie Superalgebras\",\"authors\":\"Yuqiu Sheng, Wende Liu, Yang Liu\",\"doi\":\"10.1155/2024/6650997\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this paper, we give the forms of local automorphisms (resp. superderivations) of model filiform Lie superalgebra <svg height=\\\"12.9866pt\\\" style=\\\"vertical-align:-4.3507pt\\\" version=\\\"1.1\\\" viewbox=\\\"-0.0498162 -8.6359 23.1172 12.9866\\\" width=\\\"23.1172pt\\\" xmlns=\\\"http://www.w3.org/2000/svg\\\" xmlns:xlink=\\\"http://www.w3.org/1999/xlink\\\"><g transform=\\\"matrix(.013,0,0,-0.013,0,0)\\\"></path></g><g transform=\\\"matrix(.0091,0,0,-0.0091,8.294,3.132)\\\"></path></g><g transform=\\\"matrix(.0091,0,0,-0.0091,12.953,3.132)\\\"></path></g><g transform=\\\"matrix(.0091,0,0,-0.0091,15.11,3.132)\\\"></path></g></svg> in the matrix version. Linear 2-local automorphisms (resp. superderivations) of <svg height=\\\"12.9866pt\\\" style=\\\"vertical-align:-4.3507pt\\\" version=\\\"1.1\\\" viewbox=\\\"-0.0498162 -8.6359 23.1172 12.9866\\\" width=\\\"23.1172pt\\\" xmlns=\\\"http://www.w3.org/2000/svg\\\" xmlns:xlink=\\\"http://www.w3.org/1999/xlink\\\"><g transform=\\\"matrix(.013,0,0,-0.013,0,0)\\\"><use xlink:href=\\\"#g113-77\\\"></use></g><g transform=\\\"matrix(.0091,0,0,-0.0091,8.294,3.132)\\\"><use xlink:href=\\\"#g50-111\\\"></use></g><g transform=\\\"matrix(.0091,0,0,-0.0091,12.953,3.132)\\\"><use xlink:href=\\\"#g50-45\\\"></use></g><g transform=\\\"matrix(.0091,0,0,-0.0091,15.11,3.132)\\\"><use xlink:href=\\\"#g50-110\\\"></use></g></svg> are also characterized. We prove that each linear 2-local automorphism of <svg height=\\\"12.9866pt\\\" style=\\\"vertical-align:-4.3507pt\\\" version=\\\"1.1\\\" viewbox=\\\"-0.0498162 -8.6359 23.1172 12.9866\\\" width=\\\"23.1172pt\\\" xmlns=\\\"http://www.w3.org/2000/svg\\\" xmlns:xlink=\\\"http://www.w3.org/1999/xlink\\\"><g transform=\\\"matrix(.013,0,0,-0.013,0,0)\\\"><use xlink:href=\\\"#g113-77\\\"></use></g><g transform=\\\"matrix(.0091,0,0,-0.0091,8.294,3.132)\\\"><use xlink:href=\\\"#g50-111\\\"></use></g><g transform=\\\"matrix(.0091,0,0,-0.0091,12.953,3.132)\\\"><use xlink:href=\\\"#g50-45\\\"></use></g><g transform=\\\"matrix(.0091,0,0,-0.0091,15.11,3.132)\\\"><use xlink:href=\\\"#g50-110\\\"></use></g></svg> is an automorphism.\",\"PeriodicalId\":54214,\"journal\":{\"name\":\"Journal of Mathematics\",\"volume\":\"9 1\",\"pages\":\"\"},\"PeriodicalIF\":1.3000,\"publicationDate\":\"2024-03-27\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Mathematics\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1155/2024/6650997\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Mathematics","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1155/2024/6650997","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
Local Automorphisms and Local Superderivations of Model Filiform Lie Superalgebras
In this paper, we give the forms of local automorphisms (resp. superderivations) of model filiform Lie superalgebra in the matrix version. Linear 2-local automorphisms (resp. superderivations) of are also characterized. We prove that each linear 2-local automorphism of is an automorphism.
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Journal of Mathematics is a broad scope journal that publishes original research articles as well as review articles on all aspects of both pure and applied mathematics. As well as original research, Journal of Mathematics also publishes focused review articles that assess the state of the art, and identify upcoming challenges and promising solutions for the community.
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