Cluster-tilted algebras without clusters

被引：7

作者：

Assem, Ibrahim ^{[2
]}

Bruestle, Thomas ^{[2
,3
]}

Schiffler, Ralf ^{[1
]}

机构：

[1] Univ Connecticut, Dept Math, Storrs, CT 06269 USA

[2] Univ Sherbrooke, Dept Math, Sherbrooke, PQ J1K 2R1, Canada

[3] Bishops Univ, Dept Math, Lennoxville, PQ J1M 1Z7, Canada

来源：

JOURNAL OF ALGEBRA | 2010年 / 324卷 / 09期

基金：

美国国家科学基金会; 加拿大自然科学与工程研究理事会;

关键词：

Cluster-tilted algebra; Cluster repetitive algebra; Reflections of tilted algebras; TRIVIAL EXTENSIONS;

D O I：

10.1016/j.jalgebra.2010.07.035

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We investigate the fibres of the surjective map from the class of tilted algebras to the class of cluster-tilted algebras given by forming the relation extension of tilted algebras. We introduce the notions of reflections and coreflections of tilted algebras and use them to construct all the tilted algebras in the fibre of a given cluster-tilted algebra in the case where the cluster-tilted algebra admits a local slice of tree type. Moreover, we give an explicit algorithm for the construction of the transjective component of the Auslander-Reiten quiver of the cluster-tilted algebra. (C) 2010 Elsevier Inc. All rights reserved.

引用

页码：2475 / 2502

页数：28

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