Derivation Algebra And Automorphism Group Of F[x,y]

Leibniz algebras and associative dialgebras as generalizations of Lie algebras and associative algebras have been studied in many papers since 1993.They are more connected with homology,K-Theory and Lie algebras.In this paper,some elementary definitions and properties of Leibniz algebra and associative dialgebra are discussed.We deal with derivations and automorphisms of F[x,y]as Leibniz algebra and associative dialgebras by providing the constructrue of Leibniz algebra and associative dialgebras on F[x,y].We determine all left derivations,right derivations and derivations of F[x,y]as associative dialgebra.Meanwhile, we also provide some special automorphisms of F[x,y]as associative algebra and Leibniz algebra,respectively.