Temel Weitzenböck türevleri

Consider a field K of characteristic 0 and X_n={x_1,…,x_n } as a finite set of variables. Now let F_n be the free metabelian Lie algebra and P_n be the free metabelian Poisson algebra of rank n generated by X_n over the field K. In this dissertation, initially, a set generator of the algebra F_5^δ of constants was given for a linear nilpotent derivation δ:x_5⟶x_4⟶0, δ:x_3⟶x_2⟶x_1⟶0. Secondly, the algebra P_2n^δ of constants in free metabelian Poisson algebra was determined, where δ:x_2i⟶x_(2i-1)⟶0, 1≤i≤n. Finally, the algebra P_n^(S_n ) of invariants of the symmetric group S_n was determined.