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Keywords
(2)
Cluster Algebra
Representations of Quivers
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Quivers with potentials and their representations II
Quivers with potentials and their representations II,10.1090/S0894034710006624,Journal of The American Mathematical Society,Harm Derksen,Jerzy Wey
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Quivers with potentials and their representations II
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Citations: 39
)
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Harm Derksen
,
Jerzy Weyman
,
Andrei Zelevinsky
We continue the study of quivers with potentials and their representations initiated in the first paper of the series. Here we develop some applications of this theory to cluster algebras. As shown in the ``Cluster algebras IV'' paper, the
cluster algebra
structure is to a large extent controlled by a family of integer vectors called {g} vectors, and a family of integer polynomials called F polynomials. In the case of skewsymmetric exchange matrices we find an interpretation of these {g} vectors and F polynomials in terms of (decorated)
representations of quivers
with potentials. Using this interpretation, we prove most of the conjectures about {g} vectors and F polynomials made in loc. cit.
Journal:
Journal of The American Mathematical Society  J AMER MATH SOC
, vol. 23, no. 3, pp. 749790, 2010
DOI:
10.1090/S0894034710006624
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Citation Context
(5)
...This allows us to establish the link to previous approaches, especially to the one based on the cluster category and the one based on decorated representations [36] [12] [
11
]...
...This was previously proved in [3] and [
11
]...
Bernhard Keller
,
et al.
Derived equivalences from mutations of quivers with potential
...More recently, Derksen et al. [18,
19
] have obtained a farreaching generalization of [53]...
Laurent Demonet
.
Categorification of Skewsymmetrizable Cluster Algebras
...This conjecture was proven in [
3
]f or the case when B 0 is skewsymmetric, and also in [9] in the situation where the cluster algebra admits a certain categorification...
...The next two propositions are an immediate consequence of Proposition 5.7 and Corollary 5.8 of [
3
]:...
...This formula was given in [
3
] in terms of representations of quivers with potentials...
...We recall some notation and definitions from [
3
], omitting certain technical details which are not needed here...
...A certain linear map γk : Mout(k) → Min(k) was defined in [
3
]...
...Proof The proposition follows immediately from Theorem 5.1 and Proposition 5.7 of [
3
]...
Thao Tran
.
FPolynomials in Quantum Cluster Algebras
...For their studies the Euler characteristics of a class of projective varieties, called quiver Grassmannians, are important (see [5,
10
])...
Nicolas Haupt
.
Euler Characteristics of Quiver Grassmannians and RingelHall Algebras...
...Though mainly combinatorial in their conception, many important questions about cluster algebras were answered by introducing some extra structure like for example a “categorification” [
9
,14 ]o r some Poisson geometric context [19]...
Michael Barot
,
et al.
Tubular cluster algebras I: categorification
References
(19)
On fixed point schemes of actions of multiplicative and additive groups
(
Citations: 12
)
A BialynickiBirula
Journal:
Topology
, vol. 12, no. 1, pp. 99103, 1973
Mutation of clustertilting objects and potentials
(
Citations: 28
)
Aslak Bakke Buan
,
Osamu Iyama
,
Idun Reiten
,
David Smith
Published in 2008.
Denominators of cluster variables
(
Citations: 9
)
Aslak Bakke Buan
,
Robert J. Marsh
,
Idun Reiten
Journal:
Journal of The London Mathematical Societysecond Series  J LONDON MATH SOCSECOND SER
, vol. 79, no. 3, pp. 589611, 2009
Minimal Resolutions of Algebras
(
Citations: 36
)
M. C. R. Butler
,
A. D. King
Journal:
Journal of Algebra  J ALGEBRA
, vol. 212, no. 1, pp. 323362, 1999
Cluster algebras as Hall algebras of quiver representations
(
Citations: 97
)
Philippe Caldero
,
Frederic Chapoton
Published in 2004.
Sort by:
Citations
(39)
Quiver Grassmannians associated with string modules
(
Citations: 6
)
Giovanni Cerulli Irelli
Journal:
Journal of Algebraic Combinatorics  J ALGEBR COMB
, vol. 33, no. 2, pp. 259276, 2011
Anabolic Status and Functional Impairment in Men With Mild Chronic Heart Failure
Francisco J. PastorPérez
,
Sergio ManzanoFernández
,
Iris P. Garrido Bravo
,
Francisco Nicolás
,
Pedro L. Tornel
,
Antonio Lax
,
Gonzalo de la Morena
,
Mariano Valdés
,
Domingo A. PascualFigal
Journal:
American Journal of Cardiology  AMER J CARDIOL
, vol. 108, no. 6, pp. 862866, 2011
Effect of Clopidogrel Pretreatment on Ischemic Complications of Percutaneous Coronary Intervention Among BivalirudinTreated Patients (from the EVENT Registry)
Amit P. Amin
,
Kevin F. Kennedy
,
Michael Pencina
,
Peter Berger
,
Robert N. Piana
,
John Lopez
,
Neal Kleiman
,
David J. Cohen
Journal:
American Journal of Cardiology  AMER J CARDIOL
, vol. 107, no. 12, pp. 17511756, 2011
Comparison of Medically Versus Surgically Treated Acute Type A Aortic Dissection in Patients <80 Years Old Versus Patients ≥80 Years Old
Satoshi Yanagisawa
,
Takeshi Yuasa
,
Noriyuki Suzuki
,
Toshihisa Hirai
,
Nobuyuki Yasuda
,
Ken Miki
,
Kenzo Yasuura
,
Kazutaka Horiuchi
,
Toshikazu Tanaka
Journal:
American Journal of Cardiology  AMER J CARDIOL
, vol. 108, no. 3, pp. 453459, 2011
Predictors and Implications of Coronary Infarct Artery Patency at Initial Angiography in Patients With Acute Myocardial Infarction (from the CADILLAC and HORIZONSAMI Trials)
Sorin J. Brener
,
Roxana Mehran
,
Bruce R. Brodie
,
Giulio Guagliumi
,
Bernhard Witzenbichler
,
Ecaterina Cristea
,
Ke Xu
,
Alexandra J. Lansky
,
Gregg W. Stone
Journal:
American Journal of Cardiology  AMER J CARDIOL
, vol. 108, no. 7, pp. 918923, 2011