Biderivations and linear commuting maps on the restricted Cartan-type Lie algebras and

Abstract

ABSTRACTLet and denote the restricted Cartan-type Lie algebras and in a field of characteristic , respectively. We prove that each anti-symmetric biderivation of and is inner. As applications of the anti-symmetric biderivations, it is shown that commuting maps on and are scalar multiplication maps. Moreover, we prove that the commuting automorphisms and dertivations of and are the identity mappings and zero mappings, respectively.