Derivation Algebra And Automorphism Group Of F[x,y,x^-1,y^-1]

In this paper, we define a new associative dialgebra and Leibniz algebra over a Laurent polynomial algebra with two variables x and y over a field F with charF=O. Firstly, left derivations, right derivations, derivations, inner derivations and automor-phisms of F[x,y,x-1,y-1] as an associative dialgebra are determined. Then we deter-mine all homogeneous derivations of F[x, y, x-1, y-1] as a Leibniz algebra and discuss its automorphism group.