Partial flag varieties and preprojective algebras

被引：76

作者：

Geiss, Christof ^{[1
]}

Leclerc, Bernard ^{[2
]}

Schroeer, Jan ^{[3
]}

机构：

[1] Univ Nacl Autonoma Mexico, Inst Matemat, Mexico City 04510, DF, Mexico

[2] Univ Caen, LMNO, UMR 6139, F-14032 Caen, France

[3] Univ Bonn, Math Inst, D-53115 Bonn, Germany

来源：

ANNALES DE L INSTITUT FOURIER | 2008年 / 58卷 / 03期

关键词：

flag variety; preprojective algebra; Frobenius category; rigid module; mutation; cluster algebra; semicanonical basis;

D O I：

10.5802/aif.2371

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let A be a preprojective algebra of type A, D, E, and let G be the corresponding semisimple simply connected complex algebraic group. We study rigid modules in subcategories Sub Q for Q an injective A-module, and we introduce a mutation operation between complete rigid modules in Sub Q. This yields cluster algebra structures on the coordinate rings of the partial flag varieties attached to G.

引用

页码：825 / 876

页数：52

共 32 条

[1] ALMOST SPLIT-SEQUENCES IN SUBCATEGORIES [J].

AUSLANDER, M ;

SMALO, SO .

JOURNAL OF ALGEBRA, 1981, 69 (02) :426-454

[2]

Auslander M., 1992, London Mathematical Society Lecture Note Series, V168, P1

[3]

Bautista R., 1979, P C RING THEOR ANTW, P385

[4] Cluster algebras III: Upper bounds and double Bruhat cells [J].

Berenstein, A ;

Fomin, S ;

Zelevinsky, A .

DUKE MATHEMATICAL JOURNAL, 2005, 126 (01) :1-52

[5]

BOREL A, 1991, LINEAR ALGEBRAIC GRO

[6]

BOURBAKI N, 1968, GROUPES ALGEBRES LIE, pCH4

[7]

BUAN A, 2001, ARXIVMATHRT0701557

[8] 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

[9] Double Bruhat cells and total positivity [J].

Fomin, S ;

Zelevinsky, A .

JOURNAL OF THE AMERICAN MATHEMATICAL SOCIETY, 1999, 12 (02) :335-380

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

Fomin, S ;

Zelevinsky, A .

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

← 1 2 3 4 →