Isomorphism theorems for crossed squares of Lie algebras and their morphisms

This thesis on isomorphism theorems of crossed modules and crossed squares of Lie algebras consists of five chapters. In the first part of the thesis, the necessary information and the literature are given. In the second part, some basic concepts that are used in Lie algebras are given, and also some necessary theorems are stated and proven. In the third part, the concept of crossed module of Lie algebras is defined, crossed module homomorphism of Lie algebras and their kernels and images are given. Lie subcros-sed modules of the crossed modules of Lie algebras, Lie crossed ideals and quotient cros-sed modules of Lie algebras are investigated. Also, isomorphism theorems for crossed mo-dules of Lie algebras are stated and proven. In the fourth part, using the definition of crossed squares of Lie algebras, the con-cepts defined and the theorems given in the third chapter are stated and proven by means of the necessary properties of the structure. In the last part, the results obtained are interpreted, literature gains are mentioned, and also ideas about some future studies are expressed.