Super Kupershmidt operators and Kupershmidt-Nijenhuis structures on Malcev superalgebras

Abstract

In this paper, we focus on the super Kupershmidt operators (also called super $\mathcal{O}$-operators or relative Rota-Baxter operators) of a Malcev superalgebra. We first consider the relationship between Nijenhuis operators and super Kupershimidt operators. Then we discuss Kupershmidt-(dual-)Nijenhuis structures on a Malcev superalgebra. Moreover, we study the deformations of Nijenhuis elements and obtain a deformation theory of super Kupershmidt operators on a Malcev superalgebra.

Communicated by Alberto Elduque

Keywords:

• Deformation
• (dual)-Nijenhuis pair
• Kupershmidt-(dual-)Nijenhuis structure
• Malcev superalgebra
• super Kupershmidt operator

2020 Mathematics Subject Classification:

• 17B10; 17D10; 17B60

Additional information

Funding

Supported by NSF of Jilin Province (No. YDZJ202201ZYTS589), NNSF of China (Nos. 12271085, 12071405) and the Fundamental Research Funds for the Central Universities.