Central test elements of free nilpotent lie algebras

In this study, the test elements of central automorphisms, which are a special group of automorphisms of free nilpotent Lie algebras, were investigated. This thesis consists of 6 parts. In the first part, information about the thesis is given. In the second part, the basic definitions and theorems that we will use throughout the study are given. In the third part, important definitions about algebra and Lie algebra are given. In the fourth part, information about the structure of the central automorphism group of the free nilpotent Lie algebra has been compiled from the previous studies. In the fifth part, the central test set and the central test elements of the L_(m,n) free nilpotent Lie algebra were defined and the central test sets were obtained for m=2,3 and n≤5. In the last part, a brief evaluation of the studies done in the thesis is made. In addition, the work that can be done in the future is briefly mentioned.