SIFAT-SIFAT REPRESENTASI QUIVER SEDERHANA

V Y Kurniawan

Abstract


Graf berarah dapat dipandang sebagai pasangan 4-tupel yang terdiri dari dua himpunan serta dua pemetaan dan disebut sebagai quiver . Untuk suatu quiver dapat didefinisikan representasi quiver . Representasi quiver merupakan penempatan ruang vektor pada setiap titik-titik dari quiver dan pemetaan linier pada setiap panah-panahnya. Sebuah representasi yang tidak memiliki subrepresentasi sejati selain nol disebut sebagai representasi sederhana. Pada makalah ini, dipelajari sifat-sifat dari suatu representasi quiver sederahana. Selanjutnya sifat-sifat tersebut digunakan untuk menyelidiki syarat perlu dan cukup dari suatu representasi sederhana.

A directed graph can be viewed as a 4-tuple where are finite sets of vertices and arrows respectively, and are two maps from to . A directed graph is often called a quiver. For a quiver , we can define a quiver representation . 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. In this paper, we study the properties of a simple representation of quiver. These properties will be used to investigate the necessary and sufficient condition of a simple representation of quiver.


Keywords


Morphism; Quiver; Simple Representation; Subrepresentation.

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References


Barot M. 2006. Representations of Quivers, Notes for The ICTP-Conference. Instituto de Matmticas Universidad Nacional Autnoma de Mxico. Mexico: Ciudad Universitaria.

Brion M. 2008. Representations of Quivers, Notes de lcole dt Geometric Methods in Representation Theory. Grenoble.

David A N. 2015. Cyclic symmetries of An-quiver representations, Advances in Mathematics Vol. 269: 346-363.

Derksen H & Weyman J. 2005. Quiver Representations. Notice of The AMS 52 (2): 200-206.

Krause H. 2007 Representations of Quivers via Reflection Functor. Institut Fur Mathematik, Universitat Paderborn, Paderborn, Germany.

Riedtmann C. 2016 Explicit description of generic representations for quivers of type or , Journal of Algebra 452: 474-486.

Steve YO. 2015. Persistence Theory: From Quiver Representations to Data Analysis (Mathematical Surveis and Monographs, American Mathematical Society, United State of America.

Weist T. 2015. On the recursive construction of indecomposable quiver, Journal of Algebra 443: 49-74.


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