ALJABAR LINTASAN ATAS LAPANGAN DAN REPRESENTASI QUIVER
| Main Authors: | , VIKA YUGI KURNIAWAN, , Dr.rer.nat Indah Emilia Wijayanti, M.Si. |
|---|---|
| Format: | Thesis NonPeerReviewed |
| Terbitan: |
[Yogyakarta] : Universitas Gadjah Mada
, 2012
|
| Subjects: | |
| Online Access: |
https://repository.ugm.ac.id/100984/ http://etd.ugm.ac.id/index.php?mod=penelitian_detail&sub=PenelitianDetail&act=view&typ=html&buku_id=57890 |
Daftar Isi:
- On any quiver ô��3and a field ô��, we can define a ô��-algebra which is called a path algebra ô��ô��3. This path algebra has a basis that is the set of all paths in the quiver. Conversely, a finite dimensional algebra ô��£can be obtained by a quiver ô��3ô�®o. Furthermore, a quiver representation â�� = (ô�� ̧ô� ̄� , ô���ô�°�) can be formed on any quiver. A representation of a quiver ô��3is 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 ô�� ̧and ô��1 are the representations of quiver ô��3, then it can be formed a new representation which is called a direct sum of V and W and denoted by ô�� ̧â ̈�ô��1. A representation â�� of the quiver ô��3is called indecomposable representation if â�� is not isomorphic to a direct sum of two nonzero representations. In this thesis, we study the properties of a representation quiver â��. Moreover, we investigate the necessary and sufficient condition of a representation quiver â�� to be a simple representation and indecomposable representation.