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 g to a g -module M. Then we prove that a super-biderivation from g to M is a sum of a supersymmetric super-biderivation from g to M and a skew-supersymmetric super-biderivation from g to M. Finally, we also determine the super-biderivations from s l ( 2 , 1 ) to all simple modules of s l ( 2 , 1 ) .