Crossed corner of Lie algebras and related structures

This master thesis entitled "Crossed Corner of Lie Algebras and Related Structures" consists of three chapters. In the first chapter, definitions of lie algebras, crossed modules of Lie algebras are given. In the second chapter, by defining the crossed corner of Lie algebras, it has been shown that their actions are well defined and it has been shown the category of reduced simplicial lie algebras with a Moore complex of length 2 is equivalent to the category of crossed corners of lie algebras. In the last section, the results obtained are given and suggestions are made for individuals who want to work on this subject in the future. Keywords: Crossed Corner, Crossed Module, Simplicial Lie Algebra