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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| Soggetti: | |
| Accesso online: | https://arxiv.org/abs/2510.26206 |
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| _version_ | 1866918178845622272 |
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| author | Tomonaga, Ryu |
| author_facet | Tomonaga, Ryu |
| contents | A $d$-silting object is a silting object whose derived endomorphism algebra has global dimension $d$ or less. We give an equivalent condition, which can be stated in terms of dg quivers, for silting mutations to preserve the $d$-siltingness under a mild assumption. Moreover, we show that this mild assumption is always satisfied by $ν_d$-finite algebras.
As an application, we give a counterexample to the open question by Herschend-Iyama-Oppermann: the quivers of higher hereditary algebras are acyclic. Our example is a $2$-representation tame algebra with a $2$-cycle which is derived equivalent to a toric Fano stacky surface. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_26206 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On silting mutations preserving global dimension Tomonaga, Ryu Representation Theory Rings and Algebras A $d$-silting object is a silting object whose derived endomorphism algebra has global dimension $d$ or less. We give an equivalent condition, which can be stated in terms of dg quivers, for silting mutations to preserve the $d$-siltingness under a mild assumption. Moreover, we show that this mild assumption is always satisfied by $ν_d$-finite algebras. As an application, we give a counterexample to the open question by Herschend-Iyama-Oppermann: the quivers of higher hereditary algebras are acyclic. Our example is a $2$-representation tame algebra with a $2$-cycle which is derived equivalent to a toric Fano stacky surface. |
| title | On silting mutations preserving global dimension |
| topic | Representation Theory Rings and Algebras |
| url | https://arxiv.org/abs/2510.26206 |