On a Partial Order of Tilting Modules

By D. Happel, L. Unger. 2005

118 citations recorded by the source corpus.

Subfields: Algebra and Number Theory, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/7e6c51025889664a03ff85e75dcbdf18eb2ea91d

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Algebra and Number Theory

1. B. Keller
2. I. Reiten
3. Osamu Iyama
4. Bernard Leclerc
5. Gustavo Jasso
6. C. Geiss
7. J. Schröer
8. Dong Ping Yang

In Geometry and Topology

1. B. Keller
2. Osamu Iyama
3. I. Reiten
4. Bernard Leclerc
5. Gustavo Jasso
6. C. Geiss
7. J. Schröer
8. Pierre-Guy Plamondon

Citations in the corpus

• Silting mutation in triangulated categories (2010, methodology): “It has been shown by Happel–Unger [17] that ‘tilting mutation’ is closely related to the partial order of tilting modules given by the inclusion relation of the associated t-structures, and this is a big advantage of ‘tilting mutation’ which ‘cluster tilting mutation’ and ‘exceptional mutation’ do n”
• Triangulated Categories: Cluster algebras, quiver representations and triangulated categories (2008, unknown): “1]. 2) Each rigid indecomposable is contained in a cluster-tilting set. Any two cluster-tilting sets are linked by a finite sequence of mutations. This is deduced in [10] from the work of Happel-Unger [78]. 3) If (T1,T∗ 1 ) is an exchange pair and T∗ 1→E →T →ΣT∗ 1and T →E′ →T∗ 1 →ΣT are the exchange ”
• Fomin-Zelevinsky mutation and tilting modules over Calabi-Yau algebras (2006, methodology): “The following easy lemma is useful (e.g. [ HU2 ;1.2], [Ye2;2.3]).”
• Cluster algebra structures and semicanonical bases for unipotent groups (2007, background): “Here are some known facts: (a) If T and Rare basic tilting modules satisfying (i), then there is an arrow T→R or R→Tin KA; (b) The quiver KA is the Hasse quiver of the partially order set (TA,≤), see [HU2]; (c) If there is an arrow T→Rin KA, then R≤Tand proj.dim(R) ≥proj.dim(T); (d) If R∈T⊥, then R≤”
• Reduction of τ-Tilting Modules and Torsion Pairs (2013, background): “Also, Happel and Unger showed in [16] that tilting mutation is intimately related to the partial order of tilting modules induced by the inclusion of the associated torsion classes.”
• Derived equivalences from mutations of quivers with potential (2009, background): “llowing lemma is well-known tothe experts in tilting theory although it is noteasy to point to a specific reference. One could cite Auslander-Platzeck-Reiten [2], Riedtmann-Schofield [42], Happel-Unger [24], Buan-Marsh-Reineke-Reiten-Todorov [4], Geiss-Leclerc-Schr¨oer [20] and many others. Let Tbe a ”
• The classification of \tau-tilting modules over Nakayama algebras (2013, background): “ucture of a partially ordered set (poset, for short), and the Hasse quiver of this poset coincides with the mutation quiver of support τ-tilting modules. This is an analog of a result by Happel-Unger [HU] for tilting modules. It is also known that there are close relationships between τ-tilting modu”
• Lattice structure of torsion classes for path algebras (2013, background): “A related partial order has been studied in classical tilting theory by many authors (for example, [2, 6, 8, 11]).”