Maximal $\tau_d$-rigid pairs
| Autor: | Jacobsen, Karin M., Jorgensen, Peter |
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| Rok vydání: | 2018 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1016/j.jalgebra.2019.10.046 |
| Popis: | Let $\mathscr T$ be a $2$-Calabi--Yau triangulated category, $T$ a cluster tilting object with endomorphism algebra $\Gamma$. Consider the functor $\mathscr T( T,- ) : \mathscr T \rightarrow \mod \Gamma$. It induces a bijection from the isomorphism classes of cluster tilting objects to the isomorphism classes of support $\tau$-tilting pairs. This is due to Adachi, Iyama, and Reiten. The notion of $( d+2 )$-angulated categories is a higher analogue of triangulated categories. We show a higher analogue of the above result, based on the notion of maximal $\tau_d$-rigid pairs. Comment: 13 pages. This is the final version, accepted for publication in the Journal of Algebra |
| Databáze: | arXiv |
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