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Product and complex structures on hom-Lie superalgebras
Communications in Algebra ( IF 0.6 ) Pub Date : 2021-04-01 , DOI: 10.1080/00927872.2021.1902533 Ying Hou 1 , Liming Tang 2 , Liangyun Chen 1
中文翻译:
hom-Lie 超代数上的积和复结构
更新日期:2021-04-01
Communications in Algebra ( IF 0.6 ) Pub Date : 2021-04-01 , DOI: 10.1080/00927872.2021.1902533 Ying Hou 1 , Liming Tang 2 , Liangyun Chen 1
Affiliation
Abstract
In this article, we introduce the product structures and complex structures on hom-Lie superalgebras. First, we give the necessary and sufficient conditions for the existence of product structures and complex structures, respectively. Then, we study special product structures and complex structures, respectively, and accordingly give different decompositions of hom-Lie superalgebras. Finally, as applications of these two structures, we introduce para-Kähler hom-Lie superalgebras and Kähler hom-Lie superalgebras and then obtain some properties.
中文翻译:
hom-Lie 超代数上的积和复结构
摘要
在本文中,我们介绍了hom-Lie 超代数的乘积结构和复结构。首先,我们分别给出了产品结构和复杂结构存在的充要条件。然后,我们分别研究了特殊的积结构和复结构,并据此给出了hom-Lie超代数的不同分解。最后,作为这两种结构的应用,我们引入了对Kähler hom-Lie 超代数和Kähler hom-Lie 超代数,并得到了一些性质。