ALJABAR LINTASAN ATAS LAPANGAN DAN REPRESENTASI QUIVER
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...
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| Format: | Thesis |
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[Yogyakarta] : Universitas Gadjah Mada
2012
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| _version_ | 1826045882301153280 |
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| author | , VIKA YUGI KURNIAWAN , Dr.rer.nat Indah Emilia Wijayanti, M.Si. |
| author_facet | , VIKA YUGI KURNIAWAN , Dr.rer.nat Indah Emilia Wijayanti, M.Si. |
| author_sort | , VIKA YUGI KURNIAWAN |
| collection | UGM |
| description | 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 �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. |
| first_indexed | 2024-03-13T22:44:28Z |
| format | Thesis |
| id | oai:generic.eprints.org:100984 |
| institution | Universiti Gadjah Mada |
| last_indexed | 2024-03-13T22:44:28Z |
| publishDate | 2012 |
| publisher | [Yogyakarta] : Universitas Gadjah Mada |
| record_format | dspace |
| spelling | oai:generic.eprints.org:1009842016-03-04T08:49:16Z https://repository.ugm.ac.id/100984/ ALJABAR LINTASAN ATAS LAPANGAN DAN REPRESENTASI QUIVER , VIKA YUGI KURNIAWAN , Dr.rer.nat Indah Emilia Wijayanti, M.Si. ETD 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. [Yogyakarta] : Universitas Gadjah Mada 2012 Thesis NonPeerReviewed , VIKA YUGI KURNIAWAN and , Dr.rer.nat Indah Emilia Wijayanti, M.Si. (2012) ALJABAR LINTASAN ATAS LAPANGAN DAN REPRESENTASI QUIVER. UNSPECIFIED thesis, UNSPECIFIED. http://etd.ugm.ac.id/index.php?mod=penelitian_detail&sub=PenelitianDetail&act=view&typ=html&buku_id=57890 |
| spellingShingle | ETD , VIKA YUGI KURNIAWAN , Dr.rer.nat Indah Emilia Wijayanti, M.Si. ALJABAR LINTASAN ATAS LAPANGAN DAN REPRESENTASI QUIVER |
| title | ALJABAR LINTASAN ATAS LAPANGAN
DAN REPRESENTASI QUIVER |
| title_full | ALJABAR LINTASAN ATAS LAPANGAN
DAN REPRESENTASI QUIVER |
| title_fullStr | ALJABAR LINTASAN ATAS LAPANGAN
DAN REPRESENTASI QUIVER |
| title_full_unstemmed | ALJABAR LINTASAN ATAS LAPANGAN
DAN REPRESENTASI QUIVER |
| title_short | ALJABAR LINTASAN ATAS LAPANGAN
DAN REPRESENTASI QUIVER |
| title_sort | aljabar lintasan atas lapangan dan representasi quiver |
| topic | ETD |
| work_keys_str_mv | AT vikayugikurniawan aljabarlintasanataslapangandanrepresentasiquiver AT drrernatindahemiliawijayantimsi aljabarlintasanataslapangandanrepresentasiquiver |