BENTUK KUADRATIK DARI SUATU QUIVER

• Main Author: K, DELSI
• Format: Theses
• Language: Indonesia
• Subjects: Matematika
• Online Access: https://digilib.itb.ac.id/gdl/view/69701
• Institution: Institut Teknologi Bandung

In this thesis we will discuss how a quiver Q corresponds to a path algebra A = KQ can represent some A-modules, and how we can determine the dimension vector of A-module and form Cartan matrix of the algebra A. Using Cartan matrix, we can dene Euler char- acteristic and Euler quadratic form of the algebra A. Then we will show that the Euler quadratic form qA of the path algebra A = KQ and the quadratic form qQ of the quiver Q coincide. The main result in this thesis is if Q is a nite, connected, acyclic quiver, Q is graph of Q, then Dynkin graph Q corresponds to positive denite quadratic form, Euclidean graph Q corresponds to positive semidenite quadratic form but not positive denite, and Q which are neither Dynkin nor Euclidean graph corresponds to indenite quadratic form.