Indecomposable representations for real roots of a wild quiver

JOURNAL OF ALGEBRA

卷:319

Article

Jensen, Bernt Tore¹  Su, Xiuping² 

[1] Univ Sherbrooke, Dept Matemat, Sherbrooke, PQ J1K 2R1, Canada

[2] Univ Bern, Inst Matemat, CH-3012 Bern, Switzerland

关键词: endomorphism ring;    real root;    reflection operation;    tree representation;   

DOI  :  10.1016/j.jalgebra.2007.09.002

来源: Elsevier

【 摘 要 】

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. (C) 2008 Elsevier Inc. All rights reserved.

【 授权许可】

Free