Discrete derived categories I: homomorphisms, autoequivalences and t-structures

被引：29

作者：

Broomhead, Nathan ^{[1
]}

Pauksztello, David ^{[2
]}

Ploog, David ^{[3
]}

机构：

[1] Leibniz Univ Hannover, Inst Algebra Geometrie, Welfengarten 1, D-30167 Hannover, Germany

[2] Univ Manchester, Sch Math, Oxford Rd, Manchester M13 9PL, Lancs, England

[3] Free Univ Berlin, Algebra Geometrie, D-14195 Berlin, Germany

来源：

MATHEMATISCHE ZEITSCHRIFT | 2017年 / 285卷 / 1-2期

基金：

英国工程与自然科学研究理事会;

关键词：

Discrete derived category; Auslander-Reiten quiver; Hom-hammock; Twist functor; Silting object; t-Structure; String algebra; TRIANGULATED CATEGORIES; ALGEBRAS; SEQUENCES; COMPLEXES; MUTATION; MAPS;

D O I：

10.1007/s00209-016-1690-1

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Discrete derived categories were studied initially by Vossieck (J Algebra 243:168-176, 2001) and later by BobiA"ski et al. (Cent Eur J Math 2:19-49, 2004). In this article, we describe the homomorphism hammocks and autoequivalences on these categories. We classify silting objects and bounded t-structures.

引用

页码：39 / 89

页数：51

共 46 条

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

Aihara, Takuma ;

Iyama, Osamu .

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

[2] Recollements and tilting objects [J].

Angeleri Hugel, Lidia ;

Koenig, Steffen ;

Liu, Qunhua .

JOURNAL OF PURE AND APPLIED ALGEBRA, 2011, 215 (04) :420-438

[3]

Anno I., ARXIV13095035

[4] The Auslander-Reiten components of Kb(proj Λ) for a cluster-tilted algebra of type (A)over-tilde [J].

Arnesen, Kristin Krogh ;

Grimeland, Yvonne .

JOURNAL OF ALGEBRA AND ITS APPLICATIONS, 2015, 14 (01)

[5] TILTED ALGEBRAS OF TYPE-AN [J].

ASSEM, I .

COMMUNICATIONS IN ALGEBRA, 1982, 10 (19) :2121-2139

[6]

Atiyah MF., 1956, Bull. Soc. Math. Fr, V84, P307, DOI [10.24033/bsmf.1475, DOI 10.24033/BSMF.1475]

[7] Classification of discrete derived categories [J].

Bobinski, Grzegorz ;

Geiss, Christof ;

Skowronski, Andrzej .

CENTRAL EUROPEAN JOURNAL OF MATHEMATICS, 2004, 2 (01) :19-49

[8] The Krull-Gabriel dimension of discrete derived categories [J].

Bobinski, Grzegorz ;

Krause, Henning .

BULLETIN DES SCIENCES MATHEMATIQUES, 2015, 139 (03) :269-282

[9] The graded centers of derived discrete algebras [J].

Bobinski, Grzegorz .

JOURNAL OF ALGEBRA, 2011, 333 (01) :55-66

[10]

BONDAL AI, 1989, MATH USSR IZV+, V53, P23

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