Mutation-acyclic quivers are totally proper
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866909866267770880 |
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| author | Neville, Scott |
| author_facet | Neville, Scott |
| contents | Totally proper quivers, introduced by S.~Fomin and the author arXiv:2406.03604, have many useful properties including powerful mutation invariants. We show that every mutation-acyclic quiver (i.e., a quiver that is mutation equivalent to an acyclic one) is totally proper. This yields new necessary conditions for a quiver to be mutation-acyclic. In particular, we show that a generalization of the Markov invariant for $3$-vertex quivers applies to all mutation-acyclic quivers. Only finitely many acyclic quivers share the same Markov invariant. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_17832 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Mutation-acyclic quivers are totally proper Neville, Scott Representation Theory Combinatorics 13F60 (Primary), 05E16, 15B36 (Secondary) Totally proper quivers, introduced by S.~Fomin and the author arXiv:2406.03604, have many useful properties including powerful mutation invariants. We show that every mutation-acyclic quiver (i.e., a quiver that is mutation equivalent to an acyclic one) is totally proper. This yields new necessary conditions for a quiver to be mutation-acyclic. In particular, we show that a generalization of the Markov invariant for $3$-vertex quivers applies to all mutation-acyclic quivers. Only finitely many acyclic quivers share the same Markov invariant. |
| title | Mutation-acyclic quivers are totally proper |
| topic | Representation Theory Combinatorics 13F60 (Primary), 05E16, 15B36 (Secondary) |
| url | https://arxiv.org/abs/2409.17832 |