Superbiderivations of Simple Modular Lie Superalgebras of Witt Type and Special Type

Abstract

Let [Formula: see text] be a simple modular Lie superealgebra of Witt type or special type over an algebraically closed field of characteristic [Formula: see text]. In this paper, all the superbiderivations of [Formula: see text] are studied. By means of weight space decompositions with respect to a suitable torus and the standard [Formula: see text]-grading structures of [Formula: see text], we show that the supersymmetric superbiderivations of [Formula: see text] are zero. Generalizing a result on the skewsymmetric biderivation of Lie algebras to the super case, we find that all the superbiderivations of [Formula: see text] are inner. As applications, the linear supercommuting maps and the supercommutative post-Lie superalgebra structures on [Formula: see text] are described.