{"title":"低维李代数的实现扩展","authors":"Iryna Yehorchenko","doi":"10.21468/scipostphysproc.14.048","DOIUrl":null,"url":null,"abstract":"We find extensions of realisations of some low-dimensional Lie algebras, in particular, for the Poincaré algebra for one space dimension. Using inequivalent extensions, we performed comprehensive classification of relative differential invariants for these Lie algebras. We show difference between classification of extensions of realisations, and classification of nonlinear realisations of Lie algebras.","PeriodicalId":355998,"journal":{"name":"SciPost Physics Proceedings","volume":" 37","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2023-11-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Extensions of realisations for low-dimensional Lie algebras\",\"authors\":\"Iryna Yehorchenko\",\"doi\":\"10.21468/scipostphysproc.14.048\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We find extensions of realisations of some low-dimensional Lie algebras, in particular, for the Poincaré algebra for one space dimension. Using inequivalent extensions, we performed comprehensive classification of relative differential invariants for these Lie algebras. We show difference between classification of extensions of realisations, and classification of nonlinear realisations of Lie algebras.\",\"PeriodicalId\":355998,\"journal\":{\"name\":\"SciPost Physics Proceedings\",\"volume\":\" 37\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2023-11-24\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"SciPost Physics Proceedings\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.21468/scipostphysproc.14.048\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"SciPost Physics Proceedings","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.21468/scipostphysproc.14.048","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Extensions of realisations for low-dimensional Lie algebras
We find extensions of realisations of some low-dimensional Lie algebras, in particular, for the Poincaré algebra for one space dimension. Using inequivalent extensions, we performed comprehensive classification of relative differential invariants for these Lie algebras. We show difference between classification of extensions of realisations, and classification of nonlinear realisations of Lie algebras.
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