{"title":"Kinematical algebras","authors":"","doi":"10.1142/9789813273610_0014","DOIUrl":"https://doi.org/10.1142/9789813273610_0014","url":null,"abstract":"","PeriodicalId":395878,"journal":{"name":"Group Theory in Physics","volume":"48 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124628049","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"FRONT MATTER","authors":"","doi":"10.1142/9789813273610_fmatter","DOIUrl":"https://doi.org/10.1142/9789813273610_fmatter","url":null,"abstract":"","PeriodicalId":395878,"journal":{"name":"Group Theory in Physics","volume":"29 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116614960","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Applications to the construction of orthonormal bases of states","authors":"","doi":"10.1142/9789813273610_0012","DOIUrl":"https://doi.org/10.1142/9789813273610_0012","url":null,"abstract":"","PeriodicalId":395878,"journal":{"name":"Group Theory in Physics","volume":"19 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125170048","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Three-dimensional Lie groups","authors":"","doi":"10.1142/9789813273610_0005","DOIUrl":"https://doi.org/10.1142/9789813273610_0005","url":null,"abstract":"","PeriodicalId":395878,"journal":{"name":"Group Theory in Physics","volume":"56 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134399991","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Representations of simple Lie algebras","authors":"","doi":"10.1142/9789813273610_0008","DOIUrl":"https://doi.org/10.1142/9789813273610_0008","url":null,"abstract":"","PeriodicalId":395878,"journal":{"name":"Group Theory in Physics","volume":"22 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116179603","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Spacetime symmetries and their representations","authors":"","doi":"10.1142/9789813273610_0013","DOIUrl":"https://doi.org/10.1142/9789813273610_0013","url":null,"abstract":"","PeriodicalId":395878,"journal":{"name":"Group Theory in Physics","volume":"17 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132472554","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Simple Lie algebras","authors":"P. Francesco, P. Mathieu, D. Sénéchal","doi":"10.1007/978-1-4612-2256-9_13","DOIUrl":"https://doi.org/10.1007/978-1-4612-2256-9_13","url":null,"abstract":"","PeriodicalId":395878,"journal":{"name":"Group Theory in Physics","volume":"122 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"117316840","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Symmetries in particles physics","authors":"","doi":"10.1142/9789813273610_0015","DOIUrl":"https://doi.org/10.1142/9789813273610_0015","url":null,"abstract":"","PeriodicalId":395878,"journal":{"name":"Group Theory in Physics","volume":"14 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131406093","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Finite groups: Basic structure theory","authors":"","doi":"10.1142/9789813273610_0003","DOIUrl":"https://doi.org/10.1142/9789813273610_0003","url":null,"abstract":"","PeriodicalId":395878,"journal":{"name":"Group Theory in Physics","volume":"34 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129545576","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Classical Lie algebras","authors":"Arun Ram","doi":"10.1142/9789813273610_0009","DOIUrl":"https://doi.org/10.1142/9789813273610_0009","url":null,"abstract":"1 Classical Lie algebras A Lie algebra is a vector space g with a bilinear map [, ] : g× g → g such that (a) [x, y] = −[y, x], for x, y ∈ g, and (b) (Jacobi identity) [x, [y, z]] + [z, [x, y]] + [y, [z, x]] = 0, for all x, y, z ∈ g. A bilinear form 〈, 〉 : g× g → C is ad-invariant if, for all x, y, z ∈ g, 〈adx(y), z〉 = −〈y, adx(z)〉, where adx(y) = [x, y], (1.1) for x, y,∈ g. The Killing form is the inner product on g given by 〈x1, x2〉 = Tr(adxady)〉. (1.2) The Jacobi identity is equivalent to the fact that the Killing form is ad-invariant. Let g be a finite dimensional Lie algebra with a nondegenerate ad-invariant bilinear form. The nondegeneracy of the form means that if {xi} be a basis of g then the dual basis {xi } of g with respect to 〈, 〉 exists. The Casimir element of g is κ = ∑","PeriodicalId":395878,"journal":{"name":"Group Theory in Physics","volume":"11 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129906279","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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