Minimal ($��$-)tilting infinite algebras
| Autor: | KAVEH MOUSAVAND, CHARLES PAQUETTE |
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| Rok vydání: | 2021 |
| Předmět: | |
| DOI: | 10.48550/arxiv.2103.12700 |
| Popis: | Motivated by a new conjecture on the behavior of bricks, we start a systematic study of minimal $��$-tilting infinite algebras. In particular, we treat minimal $��$-tilting infinite algebras as a modern counterpart of minimal representation infinite algebras and show some of the fundamental similarities and differences between these families. We then relate our studies to the classical tilting theory and observe that this modern approach can provide fresh impetus to the study of some old problems. We further show that in order to verify the conjecture it is sufficient to treat those minimal $��$-tilting infinite algebras where almost all bricks are faithful. Finally, we also prove that minimal extending bricks have open orbits, and consequently obtain a simple proof of the brick analogue of the First Brauer-Thrall Conjecture, recently shown by Schroll and Treffinger using some different techniques. Version 2 (18 pages): A short section is added to the end of the previous version in which we prove that all minimal extending bricks of functorially finite torsion classes have open orbits. From this we deduce a simple proof of the brick-analogue of the first Brauer-Thrall conjecture, recently shown by Schroll and Treffinger |
| Databáze: | OpenAIRE |
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