O-(dual-)N Structures On(Pre-)Malcev Algebras

Let M be a finite-dimensional Malcev algebra over an algebraically closed field F of characteristic 0.The main purpose of this thesis is to study O-(dual-)N structures on M and its representation V.We show that an O-(dual-)N structure gives rise to a hierarchy of pair-wise compatible O-operators.As an application,an invertible skew-symmetric r-matrix can be used to produce an r-matrix,that is compatible with it by using r-N structures un-der a certain condition and we provide a 4-dimensional example.Finally,we obtain some similar results on pre-Malcev algebras.