ALJABAR LINTASAN ATAS LAPANGAN DAN REPRESENTASI QUIVER

On any quiver �and a field �, we can define a �-algebra which is called a path algebra ��. This path algebra has a basis that is the set of all paths in the quiver. Conversely, a finite dimensional algebra �can be obtained by a quiver ��. Furthermore, a quiver representation � = (�� , ��) can be formed on any quiver. A representation of a quiver �is an assignment of a vector space to each vertex and a linear mapping to each arrow. A representation which has no proper subrepresentation except zero is called a simple representation. Furthermore, if �and � are the representations of quiver �, then it can be formed a new representation which is called a direct sum of V and W and denoted by ���. A representation � of the quiver �is called indecomposable representation if � is not isomorphic to a direct sum of two nonzero representations. In this thesis, we study the properties of a representation quiver �. Moreover, we investigate the necessary and sufficient condition of a representation quiver � to be a simple representation and indecomposable representation