ABSTRACT
Let 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.
Acknowledgements
The authors would like to thank the referee for valuable comments and suggestions on this article.
Notes
No potential conflict of interest was reported by the authors.