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19
On a cluster category of infinite Dynkin type, and the relation to triangulations of the infinitygon
 Math. Z
"... This paper investigates a certain 2CalabiYau triangulated category D whose AuslanderReiten quiver is ZA∞. We show that the cluster tilting subcategories of D form a socalled cluster structure, and we classify these subcategories in terms of ..."
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Cited by 24 (8 self)
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This paper investigates a certain 2CalabiYau triangulated category D whose AuslanderReiten quiver is ZA∞. We show that the cluster tilting subcategories of D form a socalled cluster structure, and we classify these subcategories in terms of
Ptolemy diagrams and torsion pairs in the cluster category of Dynkin type
 An, J. Algebraic Combin
"... Abstract. We give a complete classification of torsion pairs in the cluster category of Dynkin type Dn, via a bijection to new combinatorial objects called Ptolemy diagrams of type D. For the latter we give along the way different combinatorial descriptions. One of these allows us to count the numbe ..."
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Abstract. We give a complete classification of torsion pairs in the cluster category of Dynkin type Dn, via a bijection to new combinatorial objects called Ptolemy diagrams of type D. For the latter we give along the way different combinatorial descriptions. One of these allows us to count the number of torsion pairs in the cluster category of type Dn by providing their generating function explicitly. 1.
Sparseness of tstructures and negative Calabi–Yau dimension in triangulated categories generated by a spherical object
 Bull. London Math. Soc., in press
, 2012
"... Abstract. Let k be an algebraically closed field and let T be the klinear algebraic triangulated category generated by a wspherical object for an integer w. For certain values of w this category is classical. For instance, if w = 0 ..."
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Abstract. Let k be an algebraically closed field and let T be the klinear algebraic triangulated category generated by a wspherical object for an integer w. For certain values of w this category is classical. For instance, if w = 0
The modular curve as the space of stability conditions of a CY3 algebra. Preprint, available at arXiv:1111.4184
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Jørgensen: Cluster tilting vs. weak cluster tilting in Dynkin type A infinity
"... Abstract. This paper shows a new phenomenon in higher cluster tilting theory. For each positive integer d, we exhibit a triangulated category C with the following properties. On one hand, the dcluster tilting subcategories of C have very simple mutation behaviour: Each indecomposable object has exa ..."
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Abstract. This paper shows a new phenomenon in higher cluster tilting theory. For each positive integer d, we exhibit a triangulated category C with the following properties. On one hand, the dcluster tilting subcategories of C have very simple mutation behaviour: Each indecomposable object has exactly d mutations. On the other hand, the weakly dcluster tilting subcategories of C which lack functorial finiteness can have much more complicated mutation behaviour: For each 0 ≤ ` ≤ d − 1, we show a weakly dcluster tilting subcategory T ` which has an indecomposable object with precisely ` mutations.
Homotopy categories, Leavitt path algebras and Gorenstein projective modules, Algebr. Represent. Theory 17
, 2014
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TORSION PAIRS IN A TRIANGULATED CATEGORY GENERATED BY A SPHERICAL OBJECT
"... Abstract. We extend Ng’s characterisation of torsion pairs in the 2CalabiYau triangulated category generated by a 2spherical object to the characterisation of torsion pairs in the wCalabiYau triangulated category, Tw, generated by a wspherical object for any w ∈ Z. Inspired by the combinatori ..."
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Abstract. We extend Ng’s characterisation of torsion pairs in the 2CalabiYau triangulated category generated by a 2spherical object to the characterisation of torsion pairs in the wCalabiYau triangulated category, Tw, generated by a wspherical object for any w ∈ Z. Inspired by the combinatorics of Tw, we also characterise the torsion pairs in a certain wCalabiYau orbit category of the bounded derived category of the path algebra of Dynkin type A. Contents 1. Torsion pairs, extension closure and functorial finiteness 3 2. Triangulated categories generated by wspherical objects 4 3. Extensions with indecomposable outer terms in Tw for w 6 = 1 6 4. The combinatorial model and contravariantfiniteness 11
Edinburgh Research Explorer
"... Spherical subcategories in algebraic geometry Citation for published version: Hochenegger, A, Kalck, M & Ploog, D 2012 'Spherical subcategories in algebraic geometry ' ArXiv. ..."
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Spherical subcategories in algebraic geometry Citation for published version: Hochenegger, A, Kalck, M & Ploog, D 2012 'Spherical subcategories in algebraic geometry ' ArXiv.