SYARAT PERLU DAN SYARAT CUKUP AGAR REPRESENTASI QUIVER BERTIPE HINGGA
DOI:
https://doi.org/10.25077/jmu.5.4.96-105.2016Abstract
Abstrak. Teorema Gabriel, pertama kali dibuktikan oleh Gabriel pada tahun 1972 danterdiri dari dua bagian. Bagian (i) menyatakan bahwa "Suatu quiver Q adalah bertipe
hingga jika dan hanya jika setiap komponen underlying graph
b
Q adalah suatu diagram
Dynkin simply-laced" dan Bagian (ii) menyatakan "Misalkan Q suatu quiver sedemikian
sehingga
b
Q adalah suatu diagram Dynkin simply-laced. Dimensi dari suatu representasi
tak terdekomposisi (tunggal) dari Q adalah n
jika dan hanya jika n 2
adalah suatu positive root dari suatu representasi" [3]. Dalam tulisan ini akan dikaji
syarat perlu dan syarat cukup agar representasi quiver bertipe hingga. Oleh karena
itu, pada kajian ini terlebih dahulu diperkenalkan quiver dan teori representasi dengan
tujuan membuktikan Teorema Gabriel.
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