STRONGNESS OF COMPANION BASES FOR CLUSTER-TILTED ALGEBRAS OF FINITE TYPE

被引：1

作者：

Baur, Karin ^{[1
]}

Nasr-Isfahani, Alireza ^{[2
,3
]}

机构：

[1] Karl Franzens Univ Graz, Inst Math & Wissensch Rechnen, Heinrichstr 36, A-8010 Graz, Austria

[2] Univ Isfahan, Dept Math, POB 81746-73441, Esfahan, Iran

[3] Inst Res Fundamental Sci IPM, Sch Math, POB 19395-5746, Tehran, Iran

来源：

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY | 2018年 / 146卷 / 06期

基金：

奥地利科学基金会;

关键词：

Cluster-tilted algebra; companion basis; indecomposable modules; dimension vector; relation-extension algebra; root system; Euler form; QUIVERS;

D O I：

10.1090/proc/13977

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

For every cluster-tilted algebra of simply-laced Dynkin type we provide a companion basis which is strong, i.e., gives the set of dimension vectors of the finitely generated indecomposable modules for the cluster-tilted algebra. This shows in particular that every companion basis of a cluster-tilted algebra of simply-laced Dynkin type is strong. Thus we give a proof of Parsons's conjecture.

引用

页码：2409 / 2416

页数：8

共 14 条

[1] Cluster-tilted algebras as trivial extensions [J].

Assem, I. ;

Bruestle, T. ;

Schiffler, R. .

BULLETIN OF THE LONDON MATHEMATICAL SOCIETY, 2008, 40 :151-162

[2] Cluster algebras of finite type and positive symmetrizable matrices [J].

Barot, Michael ;

Ceiss, Christof ;

Zelevinsky, Andrei .

JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES, 2006, 73 :545-564

[3]

Buan AB, 2008, COMMENT MATH HELV, V83, P143

[4]

Buan AB, 2007, T AM MATH SOC, V359, P323

[5] Tilting theory and cluster combinatorics [J].

Buan, Aslak Bakke ;

Marsh, Bethany Rose ;

Reineke, Markus ;

Reiten, Idun ;

Todorov, Gordana .

ADVANCES IN MATHEMATICS, 2006, 204 (02) :572-618

[6] Quivers with relations arising from clusters (An case) [J].

Caldero, P ;

Chapoton, F ;

Schiffler, R .

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 2006, 358 (03) :1347-1364

[7] Quivers with relations and cluster tilted algebras [J].

Caldero, Philippe ;

Chapoton, Frederic ;

Schiffler, Ralf .

ALGEBRAS AND REPRESENTATION THEORY, 2006, 9 (04) :359-376

[8] Cluster algebras II: Finite type classification [J].

Fomin, S ;

Zelevinsky, A .

INVENTIONES MATHEMATICAE, 2003, 154 (01) :63-121

[9] Cluster algebras I: Foundations [J].

Fomin, S ;

Zelevinsky, A .

JOURNAL OF THE AMERICAN MATHEMATICAL SOCIETY, 2002, 15 (02) :497-529

[10]

Nakanishi Tomoki., 2014, ELECTRON J COMB, V21, P107

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