Biderivations and linear commuting maps on the restricted Cartan-type Lie algebrasH(n;1)

Let F be a field of characteristic p > 3 and H be the restricted Cartan-type Lie algebras H(n,1¯). We prove that each skew-symmetric biderivation of H is inner. As applications of the skew-symmetric biderivations, it is shown that commuting mappings on H are scalar multiplication mappings. Moreover, we prove that the commuting automorphisms and dertivations of H are the identity mappings and zero mappings, respectively.