On Maximal Green Sequences

被引：57

作者：

Bruestle, Thomas ^{[1
]}

Dupont, Gregoire ^{[2
]}

Perotin, Matthieu ^{[3
]}

机构：

[1] Univ Sherbrooke, Bishops Univ, Sherbrooke, PQ J1K 2R1, Canada

[2] Univ Paris 07, Paris, France

[3] Bull SAS, Bruyeres Le Chatel, France

来源：

INTERNATIONAL MATHEMATICS RESEARCH NOTICES | 2014年 / 2014卷 / 16期

基金：

加拿大自然科学与工程研究理事会;

关键词：

CLUSTER ALGEBRAS; SIMPLICIAL COMPLEX; QUIVERS; CATEGORIES;

D O I：

10.1093/imrn/rnt075

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Maximal green sequences are particular sequences of quiver mutations appearing in the context of quantum dilogarithm identities and supersymmetric gauge theory. Interpreting maximal green sequences as paths in various natural posets arising in representation theory, we prove the finiteness of the number of maximal green sequences for cluster finite quivers, affine quivers, and acyclic quivers with at most three vertices. We also give results concerning the possible numbers and lengths of these maximal green sequences.

引用

页码：4547 / 4586

页数：40

共 48 条

[1]

Adachi T., 2012, ARXIV12101036V2MATHR

[2] Silting mutation in triangulated categories [J].

Aihara, Takuma ;

Iyama, Osamu .

JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES, 2012, 85 :633-668

[3]

Alim M., 2011, ARXIV11123984V1HEPTH

[4] CLUSTER CATEGORIES FOR ALGEBRAS OF GLOBAL DIMENSION 2 AND QUIVERS WITH POTENTIAL [J].

Amiot, Claire .

ANNALES DE L INSTITUT FOURIER, 2009, 59 (06) :2525-2590

[5]

[Anonymous], 2007, LONDON MATH SOC LECT

[6]

Assem I., 2005, ELEMENTS REPRESENTAT, V1

[7] Gentle algebras arising from surface triangulations [J].

Assem, Ibrahim ;

Brustle, Thomas ;

Charbonneau-Jodoin, Gabrielle ;

Plamondon, Pierre-Guy .

ALGEBRA & NUMBER THEORY, 2010, 4 (02) :201-229

[8]

AUSLANDER M, 1979, T AM MATH SOC, V250, P1

[9] 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

[10] 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

← 1 2 3 4 5 →