Symmetric Biderivations on Complex Semisimple Lie Algebras

Abstract

This paper studies biderivations on finite-dimensional complex semisimple Lie algebras to their finite-dimensional modules. More precisely, we prove that all such symmetric biderivations are trivial. As applications, we determine all biderivations on Takiff algebras and symplectic oscillator algebras, as well as all supersymmetric biderivations over some Lie superalgebras including all finite-dimensional classical simple Lie superalgebras.