The biderivations of 𝔰𝔩(2,1) with coefficients in simple modules

Abstract

Over a field of characteristic $p>2$, we first provide the definitions of the supersymmetric super-biderivation and the skew-supersymmetric super-biderivation from a Lie superalgebra $\mathfrak{g}$ to a $\mathfrak{g}$-module M. Then we prove that a super-biderivation from $\mathfrak{g}$ to M is a sum of a supersymmetric super-biderivation from $\mathfrak{g}$ to M and a skew-supersymmetric super-biderivation from $\mathfrak{g}$ to M. Finally, we also determine the super-biderivations from $\mathfrak{s}\mathfrak{l}(2,1)$ to all simple modules of $\mathfrak{s}\mathfrak{l}(2,1)$.

Keywords:

• $\mathfrak{s}\mathfrak{l}(2,1)$
• the skew-supersymmetric super-biderivation
• the super-biderivation
• the supersymmetric super-biderivation

2020 Mathematics Subject Classification:

• 17B40
• 17B50

Additional information

Funding

Supported by the NSF of China (12061029, 12271345) and the NSF of Hainan Province (120RC587).