REALIZING HIGHER CLUSTER CATEGORIES OF DYNKIN TYPE AS STABLE MODULE CATEGORIES

被引：2

作者：

Holm, Thorsten ^{[1
]}

Jorgensen, Peter ^{[2
]}

机构：

[1] Leibniz Univ Hannover, Fac Math & Phys, Inst Algebra Zahlentheorie & Diskrete Math, D-30167 Hannover, Germany

[2] Newcastle Univ, Sch Math & Stat, Newcastle Upon Tyne NE1 7RU, Tyne & Wear, England

来源：

QUARTERLY JOURNAL OF MATHEMATICS | 2013年 / 64卷 / 02期

关键词：

EQUIVALENCE; ALGEBRAS; QUIVERS;

D O I：

10.1093/qmath/has013

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We show that the stable module categories of certain self-injective algebras of finite representation type having tree class A(n), D-n, E-6, E-7 or E-8 are triangulated equivalent to u-cluster categories of the corresponding Dynkin type. The proof relies on the 'Morita' theorem for u-cluster categories by Keller and Reiten, along with the recent computation of Calabi-Yau dimensions of stable module categories by Dugas.

引用

收藏

页码：409 / 435

页数：27

相关论文

共 50 条

[21] Homological Transfer between Additive Categories and Higher Differential Additive Categories [J].

Tang, Xi ;

Huang, Zhao Yong .

ACTA MATHEMATICA SINICA-ENGLISH SERIES, 2024, 40 (05) :1325-1344

[22] CLUSTER ALGEBRAS AND CLUSTER CATEGORIES [J].

Keller, B. .

BULLETIN OF THE IRANIAN MATHEMATICAL SOCIETY, 2011, 37 (02) :187-234

[23] Cluster categories of formal DG algebras and singularity categories [J].

Hanihara, Norihiro .

FORUM OF MATHEMATICS SIGMA, 2022, 10

[24] Graded mutation in cluster categories coming from hereditary categories with a tilting object [J].

Bertani-Okland, Marco Angel ;

Oppermann, Steffen ;

Wralsen, Anette .

JOURNAL OF PURE AND APPLIED ALGEBRA, 2012, 216 (12) :2783-2799

[25] On generalized cluster categories [J].

Amiot, Claire .

REPRESENTATIONS OF ALGEBRAS AND RELATED TOPICS, 2011, :1-53

[26] Quotients of cluster categories [J].

Jorgensen, Peter .

PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS, 2010, 140 :65-81

[27] Stable categories and reconstruction [J].

Rickard, Jeremy ;

Rouquier, Raphaeel .

JOURNAL OF ALGEBRA, 2017, 475 :287-307

[28] Partial Hopf module categories [J].

Alvares, Edson R. ;

Alves, Marcelo M. S. ;

Batista, Eliezer .

JOURNAL OF PURE AND APPLIED ALGEBRA, 2013, 217 (08) :1517-1534

[29] Dimer models and cluster categories of Grassmannians [J].

Baur, Karin ;

King, Alastair D. ;

Marsh, Bethany R. .

PROCEEDINGS OF THE LONDON MATHEMATICAL SOCIETY, 2016, 113 :213-260

[30] Generators in module and comodule categories [J].

Wisbauer, Robert .

RINGS, MODULES AND REPRESENTATIONS, 2009, 480 :351-361

← 1 2 3 4 5 →