SONLU BOYUTLU CEBİRLERDE AYRIŞTIRILAMAZ TEMSİLLER

The aim of this study is to examine the decompositions of indecomposable representations of \mathbb{A}_3 type quivers and to develop Python code that computes these decompositions. In the first chapter, basic information about module theory is provided, including some basic concepts necessary for quivers. In the second chapter, the definitions and fundamental properties of quivers and their representations are discussed. In the third chapter, the types of quivers are introduced. The indecomposable representations of quivers of finite type, namely \mathbb{A}_n, \mathbb{D}_n, \mathbb{E}_6, \mathbb{E}_7, \mathbb{E}_8. In the fourth chapter, the indecomposable submodules of modules and their decompositions are presented. Also, the concept of idempotent which is important for decompositions ve some of its properties are discussed. In the fifth chapter, the quadratic form of a quiver and roots are given and followed by the relationship between the quadratic form and the concept of roots. This chapter also includes Gabriel's theorem, which plays a significant role in the classification of quivers, along with its proof. In the sixth chapter, decompositions are obtained for the representations of \mathbb{A}_3 and Python code is provided for this decomposition.