{"title":"Para-Kähler and pseudo-Kähler structures on Lie–Yamaguti algebras","authors":"Jia Zhao, Yuqin Feng, Yu Qiao","doi":"10.1142/s0219498825502044","DOIUrl":null,"url":null,"abstract":"<p>For a pre-Lie–Yamaguti algebra <span><math altimg=\"eq-00001.gif\" display=\"inline\" overflow=\"scroll\"><mi>A</mi></math></span><span></span>, by using its sub-adjacent Lie–Yamaguti algebra <span><math altimg=\"eq-00002.gif\" display=\"inline\" overflow=\"scroll\"><msup><mrow><mi>A</mi></mrow><mrow><mi>c</mi></mrow></msup></math></span><span></span>, we are able to construct a semidirect product Lie–Yamaguti algebra via a representation of <span><math altimg=\"eq-00003.gif\" display=\"inline\" overflow=\"scroll\"><msup><mrow><mi>A</mi></mrow><mrow><mi>c</mi></mrow></msup></math></span><span></span>. The investigation of such semidirect Lie–Yamaguti algebras leads us to the notions of para-Kähler structures and pseudo-Kähler structures on Lie–Yamaguti algebras, and also gives the definition of complex product structures on Lie–Yamaguti algebras. Furthermore, a Levi–Civita product with respect to a pseudo-Riemannian Lie–Yamaguti algebra is introduced and we explore its relation with pre-Lie–Yamaguti algebras.</p>","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-02-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1142/s0219498825502044","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
For a pre-Lie–Yamaguti algebra , by using its sub-adjacent Lie–Yamaguti algebra , we are able to construct a semidirect product Lie–Yamaguti algebra via a representation of . The investigation of such semidirect Lie–Yamaguti algebras leads us to the notions of para-Kähler structures and pseudo-Kähler structures on Lie–Yamaguti algebras, and also gives the definition of complex product structures on Lie–Yamaguti algebras. Furthermore, a Levi–Civita product with respect to a pseudo-Riemannian Lie–Yamaguti algebra is introduced and we explore its relation with pre-Lie–Yamaguti algebras.