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

Abstract

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