BENTUK KUADRATIK DARI SUATU QUIVER
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 t...
Saved in:
| Main Author: | |
|---|---|
| Format: | Theses |
| Language: | Indonesia |
| Subjects: | |
| Online Access: | https://digilib.itb.ac.id/gdl/view/69701 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Institution: | Institut Teknologi Bandung |
| Language: | Indonesia |
| Summary: | 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. |
|---|