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Cluster mutation via quiver representations
 Comment. Math. Helv
"... Abstract. Matrix mutation appears in the definition of cluster algebras of Fomin and Zelevinsky. We give a representation theoretic interpretation of matrix mutation, using tilting theory in cluster categories of hereditary algebras. Using this, we obtain a representation theoretic interpretation of ..."
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Cited by 45 (15 self)
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Abstract. Matrix mutation appears in the definition of cluster algebras of Fomin and Zelevinsky. We give a representation theoretic interpretation of matrix mutation, using tilting theory in cluster categories of hereditary algebras. Using this, we obtain a representation theoretic interpretation of cluster mutation in case of acyclic cluster algebras.
Clustertilted algebras
 Trans. Amer. Math. Soc
"... Abstract. We introduce a new class of algebras, which we call clustertilted. They are by definition the endomorphism algebras of tilting objects in a cluster category. We show that their representation theory is very close to the representation theory of hereditary algebras. As an application of th ..."
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Cited by 31 (3 self)
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Abstract. We introduce a new class of algebras, which we call clustertilted. They are by definition the endomorphism algebras of tilting objects in a cluster category. We show that their representation theory is very close to the representation theory of hereditary algebras. As an application of this, we prove a generalised version of socalled APRtilting.
Cluster tilting for onedimensional hypersurface singularities
 Adv. Math
"... Abstract. In this article we study CohenMacaulay modules over onedimensional hypersurface singularities and the relationship with representation theory of associative algebras using methods of cluster tilting theory. We give a criterion for existence of cluster tilting objects and their complete d ..."
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Cited by 8 (7 self)
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Abstract. In this article we study CohenMacaulay modules over onedimensional hypersurface singularities and the relationship with representation theory of associative algebras using methods of cluster tilting theory. We give a criterion for existence of cluster tilting objects and their complete description by homological method using higher almost split sequences and results from birational geometry. We obtain a large class of 2CY tilted algebras which are finite dimensional symmetric and satisfies τ 2 = id. In particular, we compute 2CY tilted algebras for simple/minimally elliptic curve singuralities.
The mathematical focus of the GEAR Network
"... The mathematical focal point of the GEAR network is the interplay of topology, geometry, and dynamics on character varieties. The core mathematics, namely the theory of locally homogeneous geometric structures, flat bundles, and their deformation spaces has a long and distinguished history. The subj ..."
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The mathematical focal point of the GEAR network is the interplay of topology, geometry, and dynamics on character varieties. The core mathematics, namely the theory of locally homogeneous geometric structures, flat bundles, and their deformation spaces has a long and distinguished history. The subject has recently acquired a markedly multifaceted flavor with