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CLUSTER CATEGORIES (2010)
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by Idun Reiten
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10 - 0 self
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Citations
641
Representation theory of Artin algebras
- Auslander, Reiten, et al. - 1995
352
Tame algebras and integral quadratic forms
- Ringel - 1984
347
Elements of the Representation Theory of Associative Algebras
- Assem, Simson, et al. - 2006
237
Cluster algebras I
- Fomin, Zelevinsky
190
Electric-Magnetic Duality in Supersymmetric Non-Abelian Gauge Theories, Nucl
- Seiberg - 1995
189
Moduli spaces of local systems and higher Teichmüller theory
- Fock, Goncharov
182
On triangulated orbit categories,
- Keller - 2005
176
Quivers with potentials and their representations
- Derksen, Weyman, et al.
174
Unzerlegbare Darstellungen
- Gabriel - 1972
171
From triangulated categories to cluster algebras
- Caldero, Keller
157
Tilting in abelian categories and quasi tilted algebras
- Happel, Reiten, et al. - 1996
150
Calabi-Yau algebras
- Ginzburg
144
Cluster algebras. III. Upper bounds and double Bruhat cells
- Berenstein, Fomin, et al.
142
Cluster-tilted algebras are Gorenstein and stably
- Keller, Reiten - 2007
140
Representations of finite-dimensional algebras
- Gabriel, Rŏıter - 1992
138
Tilted algebras
- Happel
135
Cluster algebras as Hall algebras of quiver representations
- Caldero, Chapoton
118
Cluster categories for algebras of global dimension 2 and quivers with potential, Ann. Inst. Fourier 59
- Amiot - 2009
118
Mutation in triangulated categories and rigid Cohen-Macaulay modules
- Iyama, Yoshino
115
Cohen-Macaulay modules on hypersurface singularities
- Knörrer - 1987
111
Tilting theory and cluster combinatorics, Adv
- Buan, Marsh, et al.
105
Cluster structures for 2-Calabi-Yau categories and unipotent groups
- Buan, Iyama, et al.
101
Generalizations of the Bernstein-Gelfand-Ponomarev reflection functors. Representation theory
- Brenner, Butler - 1979
84
Derived equivalences from mutations of quivers with potential
- Keller, Yang
77
Toric duality is Seiberg duality
- Beasley, Plesser
71
Cluster algebras and quantum affine algebras
- Hernandez, Leclerc
71
Generalized associahedra via quiver representations
- Marsh, Reineke, et al.
67
Applications of morphisms determined by objects. In: Representation Theory of Algebras
- Auslander - 1978
64
Cluster-tilted algebras as trivial extensions
- Assem, Brüstle, et al.
64
Coxeter functors without diagrams
- Auslander, Platzeck, et al. - 1979
60
Cluster algebras and triangulated surfaces. Part I: Cluster complexes
- Fomin, Shapiro, et al. - 2006
60
Grassmannians and cluster algebras,
- Scott - 2006
56
On cluster algebras with coefficients and 2-Calabi-Yau categories
- Fu, Keller
54
Mutation of cluster-tilting objects and potentials
- Buan, Iyama, et al.
54
Cluster characters for 2-Calabi-Yau triangulated categories,
- Palu - 2008
49
algebras via cluster categories with infinitedimensional morphism spaces
- Plamondon, Cluster - 2011
48
Quivers with relations and cluster tilted algebras
- Caldero, Chapoton, et al. - 2004
46
Cluster tilted algebras of finite representation type
- Buan, Marsh, et al.
46
Cluster structures and semicanonical bases for unipotent groups
- Geiss, Leclere, et al.
44
Skew-symmetric cluster algebras of finite mutation type
- Felikson, Shapiro, et al.
40
Donaldson-Thomas theory and cluster algebras
- Nagao
39
On the quiver Grassmannian in the acyclic case
- Caldero, Reineke
38
Clusters and seeds in acyclic cluster algebras
- Buan, Marsh, et al.
37
Cluster tilting for one-dimensional hypersurface singularities,
- Burban, Iyama, et al. - 2008
36
A geometric model for cluster categories of typeDn
- Schiffler
36
Defining an m-cluster category,
- Thomas - 2007
34
A geometric description of m-cluster categories
- Baur, Marsh - 2006
34
Quantum cluster variables via Serre polynomials
- Qin
33
Representation theory of artin algebras III: Almost split sequences
- Auslander, Reiten - 1975
31
Acyclic cluster algebras via Ringel-Hall algebras, Preprint available at the author’s home
- Hubery
28
Almost complete tilting modules
- Happel
25
Cluster characters for cluster categories with infinite-dimensional morphism spaces
- Plamondon
25
Generalized cluster complexes via quiver representations, preprint
- Zhu - 2006
23
Stability structures, Donaldson–Thomas invariants and cluster transformations
- Kontsevich, Soibelman
20
Generalized cluster complexes and Coxeter
- Fomin, Reading - 2005
18
Stable categories of Cohen-Macaulay modules and cluster categories. arXiv:1104.3658
- Amiot, Iyama, et al.
16
Total positivity and cluster algebras
- Fomin
16
Cluster combinatorics of d-cluster categories,
- Zhou, Zhu - 2009
15
From tilted to cluster-tilted algebras of Dynkin type, preprint arXiv math.RT/0510445
- Buan, Reiten
15
triangulated categories to cluster algebras
- From
15
with potentials and their representations II: applications to cluster algebras
- Quivers
14
Coloured quiver mutation for higher cluster categories
- Buan, Thomas
14
algebras IV
- Cluster
13
modules over preprojective algebras
- Rigid
12
The ubiquity of generalized cluster categories,
- Amiot, Reiten, et al. - 2011
12
Cluster-tilting theory
- Buan, Marsh
12
On the combinatorics of rigid objects
- Dehy, Keller - 2008
11
Quiver varieties and cluster algebras, arXiv:0905.0002v3 [math.QA
- Nakajima
11
Tilting theory and cluster algebras, preprint available at www.institut.math.jussieu.fr/ ˜ keller/ictp2006/lecturenotes/reiten.pdf
- Reiten
11
Hypersurface singularities of finite Cohen-Macaulay type
- Solberg - 1989
10
algebras and Weil-Petersson forms
- Cluster
10
Equivalences between cluster categories
- Zhu - 2006
9
On open orbits and their complements
- Riedtmann, Schofield - 1990
8
with relations arising from clusters (An case
- Quivers
8
algebras II: Finite type classification
- Cluster - 2003
8
On the properties of the exchange graph of a cluster algebra
- Gekhtman, Shapiro, et al.
7
mutation via quiver representations
- Cluster
7
Triangulated Categories in the Representation of Finite Dimensional Algebras
- Happel - 1988
7
Cluster algebras and representation theory
- Leclerc - 2010
7
Rigid objects in higher cluster categories
- Wraalsen
6
Teichmüller and lamination spaces, Handbook of Teichmüller theory. Vol
- Dual - 2007
6
and generalized associahedra
- Y-systems
5
flag varieties and preprojective algebras, Ann
- Partial
4
bases and preprojective algebras. II. A multiplication formula
- Semicanonical
4
triangles in derived categories of finite-dimensional algebras
- Auslander-Reiten - 1991
4
Gorenstein isolated quotient singularities of odd prime dimension are cyclic
- Kurano, Nishi
3
Preprojective algebras and c-sortable words, arXiv:1002.4131
- Amiot, Iyama, et al.
3
Higher Auslander-Reiten Theory on maximal orthogonal subcategories
- Iyama
3
2-Auslander algebras associated with reduced words in Coxeter groups
- Iyama, Reiten
2
The cluster category of a canonical algebra, Trans.Amer.Math.Soc
- Barot, Kussin, et al. - 2010
2
Seven A., Tame concealed algebras and minimal infinite cluster algebras
- Buan, Reiten
2
Schur modules over wild, finite dimensional path algebras with three simple modules
- Unger - 1990
1
of cluster variables
- Denominators
1
den Bergh, Explicit modules for some stable categories of maximal Cohen-Macaulay modules, in preparation
- Völcsey, Van
1
ensembles, quantization and the dilogarithm, Ann
- Cluster
1
algebras and Poisson geometry, Mosc
- Cluster
1
quiver representations and triangulated categories, arXiv08.07.1960
- Cluster-algebras - 2006
1
triangulated categories
- Calabi-Yau
1
amassées et applications
- Algèbres