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On the Genus of the Graph of Tilting Modules Dedicated to Idun Reiten on the occasion of her 60th birthday
"... Let Λ be a finite dimensional, connected, associative algebra with unit over a field k. Let n be the number of isomorphism classes of simple Λmodules. By modΛ we denote the category of finite dimensional left Λmodules. A module ΛT ∈ modΛ is called a tilting module if (i) the projective dimension p ..."
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Let Λ be a finite dimensional, connected, associative algebra with unit over a field k. Let n be the number of isomorphism classes of simple Λmodules. By modΛ we denote the category of finite dimensional left Λmodules. A module ΛT ∈ modΛ is called a tilting module if (i) the projective dimension pd ΛT of ΛT is finite, and (ii) ExtiΛ(T, T) = 0 for all i> 0, and (iii) there is an exact sequence 0 → ΛΛ → ΛT 1 → · · · → ΛT d → 0 with ΛT i ∈ add ΛT for all 1 ≤ i ≤ d. Here add ΛT denotes the category of direct sums of direct summands of ΛT. Tilting modules play an important role in many branches of mathematics such as representation theory of Artin algebras or the theory of algebraic groups. Let m⊕ i=1 Ti be the decomposition of ΛT into indecomposable direct summands. We call
J. London Math. Soc. (2) 79 (2009) 589–611 C2009 London Mathematical Society doi:10.1112/jlms/jdn082 Denominators of cluster variables
"... J. Marsh and Idun Reiten Associated to any acyclic cluster algebra is a corresponding triangulated category known as the ..."
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J. Marsh and Idun Reiten Associated to any acyclic cluster algebra is a corresponding triangulated category known as the
ON THE ZD ∞ CATEGORY
, 2004
"... Abstract. In this paper we give a direct proof of the properties of the ZD∞ category which was introduced in the classification of noetherian, hereditary categories with Serre duality by Idun Reiten and the author. 1. ..."
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Abstract. In this paper we give a direct proof of the properties of the ZD∞ category which was introduced in the classification of noetherian, hereditary categories with Serre duality by Idun Reiten and the author. 1.
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"... Dedicated to Idun Reiten on the occasion of her seventieth birthday. Abstract. FominZelevinsky conjectured that in any cluster algebra, the cluster monomials are linearly independent and that the exchange graph is independent of the choice of coefficients. We confirm these conjectures for all skew ..."
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Dedicated to Idun Reiten on the occasion of her seventieth birthday. Abstract. FominZelevinsky conjectured that in any cluster algebra, the cluster monomials are linearly independent and that the exchange graph is independent of the choice of coefficients. We confirm these conjectures for all skew
Stable endomorphism algebras of modules over special biserial algebras
 Math. Z
"... Abstract. We prove that the stable endomorphism algebra of a module without selfextensions over a special biserial algebra is a gentle algebra. In particular, it is again special biserial. As a consequence, any algebra which is derived equivalent to a gentle algebra is gentle. Dedicated to Idun Rei ..."
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Cited by 21 (1 self)
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Abstract. We prove that the stable endomorphism algebra of a module without selfextensions over a special biserial algebra is a gentle algebra. In particular, it is again special biserial. As a consequence, any algebra which is derived equivalent to a gentle algebra is gentle. Dedicated to Idun
STANDARD DERIVED EQUIVALENCE FOR
"... Dedicated to Professor Idun Reiten on the occasion of her 60th birthday Abstract. We shall show that every stable equivalence (functor) between representationfinite selfinjective algebras not of type (D3m, s/3, 1) with m ¸ 2, 3 s lifts to a standard derived equivalence. This implies that all sta ..."
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Dedicated to Professor Idun Reiten on the occasion of her 60th birthday Abstract. We shall show that every stable equivalence (functor) between representationfinite selfinjective algebras not of type (D3m, s/3, 1) with m ¸ 2, 3 s lifts to a standard derived equivalence. This implies that all
Geometry of chain complexes and outer automorphisms under derived equivalence
 Transactions of the American Mathematical Society
"... The authors wish to dedicate this paper to Idun Reiten on the occasion of her sixtieth birthday. Abstract. The two main theorems proved here are as follows: If A is a finite dimensional algebra over an algebraically closed field, the identity component of the algebraic group of outer automorphisms o ..."
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Cited by 18 (1 self)
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The authors wish to dedicate this paper to Idun Reiten on the occasion of her sixtieth birthday. Abstract. The two main theorems proved here are as follows: If A is a finite dimensional algebra over an algebraically closed field, the identity component of the algebraic group of outer automorphisms
Torsion pairs in cluster tubes
"... Abstract. We give a complete classification of torsion pairs in the cluster categories associated to tubes of finite rank. The classification is in terms of combinatorial objects called Ptolemy diagrams which already appeared in our earlier work on torsion pairs in cluster categories of Dynkin typ ..."
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Cited by 2 (1 self)
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type A. As a consequence of our classification we establish closed formulae enumerating the torsion pairs in cluster tubes, and obtain that the torsion pairs in cluster tubes exhibit a cyclic sieving phenomenon. Dedicated to Idun Reiten on the occasion of her 70th birthday. 1.
Cotorsion pairs in the cluster category of a marked surface
 Department of Mathematics, University of Leicester, University Road, Leicester
"... Dedicated to Professor Idun Reiten on the occasion of her seventieth birthday. We study extension spaces, cotorsion pairs and their mutations in the cluster category of a marked surface without punctures. Under the onetoone correspondence between the curves, valued closed curves in the marked surf ..."
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Cited by 4 (3 self)
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Dedicated to Professor Idun Reiten on the occasion of her seventieth birthday. We study extension spaces, cotorsion pairs and their mutations in the cluster category of a marked surface without punctures. Under the onetoone correspondence between the curves, valued closed curves in the marked
− → U ′k f
"... This is the second part in a series of two lectures with Idun Reiten. We shall show that cluster tilting mutation is compatible with quiver mutation and QP mutation. Throughout let K be an algebraically closed field, and let C be a Homfinite 2CalabiYau triangulated category over K with the suspen ..."
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This is the second part in a series of two lectures with Idun Reiten. We shall show that cluster tilting mutation is compatible with quiver mutation and QP mutation. Throughout let K be an algebraically closed field, and let C be a Homfinite 2CalabiYau triangulated category over K
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