Biderivations and linear commuting maps on the restricted contact lie algebras K(n; 1)

Abstract

Let K be the restricted contact Lie algebras K(n; 1) over an algebraically closed field F of characteristic p > 3. We prove that each skew-symmetric biderivation of K is inner and show that commuting maps on K are scalar multiplication maps. Moreover, it is showed that the commuting automorphisms and dertivations of K are proved to be the identity mappings and zero mappings, respectively. Meanwhile, the commutative post-Lie algebra structures on K are given.