Super-biderivations from o s p ( 1 , 2 ) to all simple modules in prime characteristic

Abstract

In this paper, we consider the orthosymplectic Lie superalgebra o s p ( 1 , 2 ) over an algebraically closed field of characteristic p > 2 . We give a sufficient and necessary condition for a map from the cartesian product of a finite-dimensional Lie superalgebra with itself to its nontrivial and simple modules to be a symmetric super-biderivation. Finally, we determine all super-biderivations from o s p ( 1 , 2 ) to its any finite-dimensional simple module.