{"title":"关于伪厄密二次幂零李代数","authors":"Mustapha Bachaou, Ignacio Bajo, Mohamed Louzari","doi":"10.1007/s13366-023-00714-x","DOIUrl":null,"url":null,"abstract":"Abstract We study nilpotent Lie algebras endowed with a complex structure and a quadratic structure which is pseudo-Hermitian for the given complex structure. We propose several methods to construct such Lie algebras and describe a method of double extension by planes to get an inductive description of all of them. As an application, we give a complete classification of nilpotent quadratic Lie algebras where the metric is Lorentz-Hermitian and we fully classify all nilpotent pseudo-Hermitian quadratic Lie algebras up to dimension 8 and their inequivalent pseudo-Hermitian metrics.","PeriodicalId":44678,"journal":{"name":"Beitrage zur Algebra und Geometrie-Contributions to Algebra and Geometry","volume":"4 1","pages":"0"},"PeriodicalIF":0.4000,"publicationDate":"2023-09-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"On pseudo-Hermitian quadratic nilpotent lie algebras\",\"authors\":\"Mustapha Bachaou, Ignacio Bajo, Mohamed Louzari\",\"doi\":\"10.1007/s13366-023-00714-x\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Abstract We study nilpotent Lie algebras endowed with a complex structure and a quadratic structure which is pseudo-Hermitian for the given complex structure. We propose several methods to construct such Lie algebras and describe a method of double extension by planes to get an inductive description of all of them. As an application, we give a complete classification of nilpotent quadratic Lie algebras where the metric is Lorentz-Hermitian and we fully classify all nilpotent pseudo-Hermitian quadratic Lie algebras up to dimension 8 and their inequivalent pseudo-Hermitian metrics.\",\"PeriodicalId\":44678,\"journal\":{\"name\":\"Beitrage zur Algebra und Geometrie-Contributions to Algebra and Geometry\",\"volume\":\"4 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.4000,\"publicationDate\":\"2023-09-14\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Beitrage zur Algebra und Geometrie-Contributions to Algebra and Geometry\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1007/s13366-023-00714-x\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Beitrage zur Algebra und Geometrie-Contributions to Algebra and Geometry","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1007/s13366-023-00714-x","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS","Score":null,"Total":0}
On pseudo-Hermitian quadratic nilpotent lie algebras
Abstract We study nilpotent Lie algebras endowed with a complex structure and a quadratic structure which is pseudo-Hermitian for the given complex structure. We propose several methods to construct such Lie algebras and describe a method of double extension by planes to get an inductive description of all of them. As an application, we give a complete classification of nilpotent quadratic Lie algebras where the metric is Lorentz-Hermitian and we fully classify all nilpotent pseudo-Hermitian quadratic Lie algebras up to dimension 8 and their inequivalent pseudo-Hermitian metrics.
期刊介绍:
The Journal "Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry" was founded in 1971 on the occasion of the 65th birthday of O.-H. Keller. It publishes research articles in the areas of algebra, geometry, algebraic geometry and related fields, preferably in English language.
The back issues of the journal are available at the European Digital Mathematics Library (EuDML) at:
https://eudml.org/journal/10170 (Vols. 1-33, 1971-1992)
https://eudml.org/journal/10084 (Vols. 34-51, 1993-2010)