Linear Super-Commuting Maps and Super-Biderivations on the Super-Virasoro Algebras

Let SVir be the well-known super-Virasoro algebras. In this paper, we first prove that any super-skewsymmetric super-biderivation of SVir is inner. Based on this, we show that every linear super-commuting map on SVir is of the form (x)=f(x)c, where f is a linear function from SVir to C mapping the odd part of SVir to zero, and c is the central charge of SVir.