{"title":"高维空间中Clifford代数与点群的结构","authors":"S L Altmann, P. Herzig","doi":"10.1088/0305-4470/39/33/009","DOIUrl":null,"url":null,"abstract":"With the basic Clifford units being identified as mirrors, it is demonstrated how proper and improper symmetry operations of point groups in spaces of arbitrary dimensions can be parametrized. In such an approach consistency with parametrizations for groups in three dimensions can be achieved even if double groups are considered. The conversion of Clifford parameters into Cartesian matrices and vice versa is discussed and, for rotations in , also the parametrization in terms of pairs of rotations in . The formalism is illustrated by a number of examples.","PeriodicalId":87442,"journal":{"name":"Journal of physics A: Mathematical and general","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2006-08-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Clifford algebra and the structure of point groups in higher-dimensional spaces\",\"authors\":\"S L Altmann, P. Herzig\",\"doi\":\"10.1088/0305-4470/39/33/009\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"With the basic Clifford units being identified as mirrors, it is demonstrated how proper and improper symmetry operations of point groups in spaces of arbitrary dimensions can be parametrized. In such an approach consistency with parametrizations for groups in three dimensions can be achieved even if double groups are considered. The conversion of Clifford parameters into Cartesian matrices and vice versa is discussed and, for rotations in , also the parametrization in terms of pairs of rotations in . The formalism is illustrated by a number of examples.\",\"PeriodicalId\":87442,\"journal\":{\"name\":\"Journal of physics A: Mathematical and general\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2006-08-18\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of physics A: Mathematical and general\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1088/0305-4470/39/33/009\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of physics A: Mathematical and general","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1088/0305-4470/39/33/009","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Clifford algebra and the structure of point groups in higher-dimensional spaces
With the basic Clifford units being identified as mirrors, it is demonstrated how proper and improper symmetry operations of point groups in spaces of arbitrary dimensions can be parametrized. In such an approach consistency with parametrizations for groups in three dimensions can be achieved even if double groups are considered. The conversion of Clifford parameters into Cartesian matrices and vice versa is discussed and, for rotations in , also the parametrization in terms of pairs of rotations in . The formalism is illustrated by a number of examples.