Connectivity of $τ$-tilting graphs for quasi-tilted algebras and quotients of $g$-tame algebras
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866915359703957504 |
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| author | Fu, Changjian Geng, Shengfei Liu, Pin |
| author_facet | Fu, Changjian Geng, Shengfei Liu, Pin |
| contents | This note investigates the connectivity of $τ$-tilting graphs for algebras from the point of view of quotients. We establish the connectivity of $τ$-tilting graph for an arbitrary quasi-tilted algebra and prove that the connectivity of the $τ$-tilting graph of a $g$-tame algebra is preserved under quotient. In particular, quotient algebras of skew-gentle algebras and quotient algebras of tame hereditary algebras have connected $τ$-tilting graphs. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_05158 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Connectivity of $τ$-tilting graphs for quasi-tilted algebras and quotients of $g$-tame algebras Fu, Changjian Geng, Shengfei Liu, Pin Representation Theory This note investigates the connectivity of $τ$-tilting graphs for algebras from the point of view of quotients. We establish the connectivity of $τ$-tilting graph for an arbitrary quasi-tilted algebra and prove that the connectivity of the $τ$-tilting graph of a $g$-tame algebra is preserved under quotient. In particular, quotient algebras of skew-gentle algebras and quotient algebras of tame hereditary algebras have connected $τ$-tilting graphs. |
| title | Connectivity of $τ$-tilting graphs for quasi-tilted algebras and quotients of $g$-tame algebras |
| topic | Representation Theory |
| url | https://arxiv.org/abs/2401.05158 |