Product and complex structures on hom-Lie superalgebras

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.

Keywords:

• Complex structures
• hom-Lie superalgebras
• Kähler hom-Lie superalgebras
• Kähler hom-Lie superalgebras
• product structurespara

2020 MATHEMATICS SUBJECT CLASSIFICATION:

• 17A30
• 17B61
• 17D25
• 53C15
• 53D05

Additional information

Funding

This paper is supported by NNSF of China [grant nos. 11771069, 12071405 and 12001141].