Tilting-Connected Symmetric Algebras
By Takuma Aihara. 2010
102 citations recorded by the source corpus.
The notion of silting mutation was introduced by Iyama and the author. In this paper we mainly study silting mutation for self-injective algebras and prove that any representation-finite symmetric algebra is tilting-connected. Moreover we give some sufficient conditions for a Bongartz-type Lemma to hold for silting objects.
Subfields: Algebra and Number Theory, Geometry and Topology, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/2ebc0b5a3d27b452790163a360a5a4b86f674e3f
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In Algebra and Number Theory
- Gustavo Jasso
- Osamu Iyama
- Peter Jørgensen
- Yuya Mizuno
- Dong Ping Yang
- Thomas Brustle
- Aslak Bakke Buan
- Yu Zhou
In Geometry and Topology
- Gustavo Jasso
- Osamu Iyama
- Thomas Brustle
- Yuya Mizuno
- Peter Jørgensen
- Aslak Bakke Buan
- Dong Ping Yang
- Takuma Aihara
In Statistical and Nonlinear Physics
- Gustavo Jasso
- Osamu Iyama
- Aslak Bakke Buan
- Peter Jørgensen
- Yuya Mizuno
- Yu Zhou
- Thomas Brustle
- Dong Ping Yang
Citations in the corpus
- Classifying tilting complexes over preprojective algebras of Dynkin type (2015, background): “See [Aihara and Iyama 2012, Proposition 2.23, 2.24, 2.36] and [Aihara 2013, Proposition 2.12].”
- Intermediate co-t-structures, two-term silting objects, tau-tilting modules, and torsion classes (2013, background): “However, the distinguished triangle (2) induces an exact sequence T(s0 , u ) → T(s1 , u ) → T(Σu, u) → T(Σs0 , u ) where the last module is 0 since u ∈ S ∗ ΣS.”
- Reduction of τ-Tilting Modules and Torsion Pairs (2013, background): “ -siltU. is bijective. 4.2. Calabi-Yau reduction. Let Cbe a Krull-Schmidt 2-Calabi-Yau triangulated category. Thus Cis k-linear, Hom-finite and there is a bifunctorial isomorphism HomC(M,N) ∼=DHomC(N,M[2]) for every M,N ∈C, where D = Homk(−,k) is the usual k-duality. Recall that an object T in Cis ca”
- Ordered Exchange Graphs (2013, background): “It has a positive answer for C = H(projA), where A is a representation-finite symmetric algebra, see [1, 3], or A is a piecewise hereditary algebra(1).”
- A silting theorem (2015, methodology): “he analog, for 2-term silting complexes, of the Bongartz completion of classical tilting modules. It can be deduced from [AdIR, Theorem 2.10] and was proven in [Ai, DF, IJY, W]. We state the proof in [Ai] here for self-containedness. Lemma 3.1. Let P be a 2-term presilting complex in Kb(proj A). The”