Indecomposable representations for real roots of a wild quiver

Bernt Tore Jensen, Xiuping Su

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

For a given quiver and dimension vector, Kac has shown that there is exactly one indecomposable representation up to isomorphism if and only if this dimension vector is a positive real root. However, it is not clear how to compute these indecomposable representations in an explicit and minimal way, and the properties of these representations are mostly unknown. In this note we study representations of a particular wild quiver. We define operations which act on representations of this quiver, and using these operations we construct indecomposable representations for positive real roots, compute their endomorphism rings and show that these representations are tree representations. The operations correspond to the fundamental reflections in the Weyl group of the quiver. Our results are independent of the characteristic of the field.
Original languageEnglish
Pages (from-to)2271-2294
Number of pages24
JournalJournal of Algebra
Volume319
Issue number6
Early online date26 Sep 2007
DOIs
Publication statusPublished - 15 Mar 2008

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