ORIENTED FLIP GRAPHS, NONCROSSING TREE PARTITIONS, AND REPRESENTATION THEORY OF TILING ALGEBRAS
| Autor: | Thomas McConville, Alexander Garver |
|---|---|
| Rok vydání: | 2019 |
| Předmět: |
General Mathematics
010102 general mathematics Quiver 0102 computer and information sciences 01 natural sciences Representation theory Combinatorics 010201 computation theory & mathematics Bounded function Torsion (algebra) 0101 mathematics Mathematics::Representation Theory Indecomposable module Mathematics |
| Zdroj: | Glasgow Mathematical Journal. 62:147-182 |
| ISSN: | 1469-509X 0017-0895 |
| DOI: | 10.1017/s0017089519000028 |
| Popis: | The purpose of this paper is to understand lattices of certain subcategories in module categories of representation-finite gentle algebras called tiling algebras, as introduced by Coelho Simões and Parsons. We present combinatorial models for torsion pairs and wide subcategories in the module category of tiling algebras. Our models use the oriented flip graphs and noncrossing tree partitions, previously introduced by the authors, and a description of the extension spaces between indecomposable modules over tiling algebras. In addition, we classify two-term simple-minded collections in bounded derived categories of tiling algebras. As a consequence, we obtain a characterization of c-matrices for any quiver mutation-equivalent to a type A Dynkin quiver. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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