{"title":"强凯勒带扭转可解谎言数组的子维度 2 nilradical","authors":"Beatrice Brienza, Anna Fino","doi":"10.1002/mana.202400349","DOIUrl":null,"url":null,"abstract":"<p>In this paper, we study strong Kähler with torsion (SKT) and generalized Kähler structures on solvable Lie algebras with (not necessarily abelian) codimension 2 nilradical. We treat separately the case of <span></span><math>\n <semantics>\n <mi>J</mi>\n <annotation>$J$</annotation>\n </semantics></math>-invariant nilradical and non-<span></span><math>\n <semantics>\n <mi>J</mi>\n <annotation>$J$</annotation>\n </semantics></math>-invariant nilradical. A classification of such SKT Lie algebras in dimension 6 is provided. In particular, we give a general construction to extend SKT nilpotent Lie algebras to SKT solvable Lie algebras of higher dimension, and we construct new examples of SKT and generalized Kähler compact solvmanifolds.</p>","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":"297 12","pages":"4705-4729"},"PeriodicalIF":0.8000,"publicationDate":"2024-10-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/mana.202400349","citationCount":"0","resultStr":"{\"title\":\"Strong Kähler with torsion solvable lie algebras with codimension 2 nilradical\",\"authors\":\"Beatrice Brienza, Anna Fino\",\"doi\":\"10.1002/mana.202400349\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>In this paper, we study strong Kähler with torsion (SKT) and generalized Kähler structures on solvable Lie algebras with (not necessarily abelian) codimension 2 nilradical. We treat separately the case of <span></span><math>\\n <semantics>\\n <mi>J</mi>\\n <annotation>$J$</annotation>\\n </semantics></math>-invariant nilradical and non-<span></span><math>\\n <semantics>\\n <mi>J</mi>\\n <annotation>$J$</annotation>\\n </semantics></math>-invariant nilradical. A classification of such SKT Lie algebras in dimension 6 is provided. In particular, we give a general construction to extend SKT nilpotent Lie algebras to SKT solvable Lie algebras of higher dimension, and we construct new examples of SKT and generalized Kähler compact solvmanifolds.</p>\",\"PeriodicalId\":49853,\"journal\":{\"name\":\"Mathematische Nachrichten\",\"volume\":\"297 12\",\"pages\":\"4705-4729\"},\"PeriodicalIF\":0.8000,\"publicationDate\":\"2024-10-15\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://onlinelibrary.wiley.com/doi/epdf/10.1002/mana.202400349\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Mathematische Nachrichten\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://onlinelibrary.wiley.com/doi/10.1002/mana.202400349\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Mathematische Nachrichten","FirstCategoryId":"100","ListUrlMain":"https://onlinelibrary.wiley.com/doi/10.1002/mana.202400349","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
Strong Kähler with torsion solvable lie algebras with codimension 2 nilradical
In this paper, we study strong Kähler with torsion (SKT) and generalized Kähler structures on solvable Lie algebras with (not necessarily abelian) codimension 2 nilradical. We treat separately the case of -invariant nilradical and non--invariant nilradical. A classification of such SKT Lie algebras in dimension 6 is provided. In particular, we give a general construction to extend SKT nilpotent Lie algebras to SKT solvable Lie algebras of higher dimension, and we construct new examples of SKT and generalized Kähler compact solvmanifolds.
期刊介绍：
Mathematische Nachrichten - Mathematical News publishes original papers on new results and methods that hold prospect for substantial progress in mathematics and its applications. All branches of analysis, algebra, number theory, geometry and topology, flow mechanics and theoretical aspects of stochastics are given special emphasis. Mathematische Nachrichten is indexed/abstracted in Current Contents/Physical, Chemical and Earth Sciences; Mathematical Review; Zentralblatt für Mathematik; Math Database on STN International, INSPEC; Science Citation Index
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