The Classical Yang-baxter Equation Ando-operators For Malcev Algebras

In this thesis,we study connections between O-operators of a finite-dimensional Malcev algebras over a field F of characteristic zero and skew-symmetric solutions of the classical Yang-Baxter equation(CYBE).We prove that a skew-symmetric solution of the CYBE on a Malcev algebra can be interpreted as an O-operator associated to the coadjoint representation.We show that this connection can be enhanced with symplectic forms when considering non-degenerate skew-symmetric solutions.We also show that O-operators associated to a general representation give skew-symmetric solutions of the CYBE in certain semi-direct product Malcev algebras.We reveal the relationship between invertible Ooperators and compatible pre-Malcev algebra structures on a Malcev algebra.