Skew-symmetric biderivations and linear commuting maps of Kac-Moody algebras

A map phi on a Lie algebra L is called commuting if [phi(x),x]=0 for all x is an element of L. Let g be a Kac-Moody algebra over an algebraically closed field of characteristic 0. In this paper, we determine the skew-symmetric biderivations and the linear commuting maps of g. As applications, the commuting derivations and the commuting automorphisms of g are gained.