Categorifications of Non-Integer Quivers: Types $H_4$, $H_3$ and $I_2(2n+1)$
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2022
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| _version_ | 1866916316714106880 |
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| author | Duffield, Drew Damien Tumarkin, Pavel |
| author_facet | Duffield, Drew Damien Tumarkin, Pavel |
| contents | We define the notion of a weighted unfolding of quivers with real weights, and use this to provide a categorification of mutations of quivers of finite types $H_4$, $H_3$ and $I_2(2n+1)$. In particular, the (un)folding induces a semiring action on the categories associated to the unfolded quivers of types $E_8$, $D_6$ and $A_{2n}$ respectively. We then define the tropical seed pattern on the folded quivers, which includes $c$- and $g$-vectors, and show its compatibility with the unfolding. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2204_12752 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Categorifications of Non-Integer Quivers: Types $H_4$, $H_3$ and $I_2(2n+1)$ Duffield, Drew Damien Tumarkin, Pavel Representation Theory Combinatorics Rings and Algebras 13F60 (Primary), 16G70, 16G20 (Secondary) We define the notion of a weighted unfolding of quivers with real weights, and use this to provide a categorification of mutations of quivers of finite types $H_4$, $H_3$ and $I_2(2n+1)$. In particular, the (un)folding induces a semiring action on the categories associated to the unfolded quivers of types $E_8$, $D_6$ and $A_{2n}$ respectively. We then define the tropical seed pattern on the folded quivers, which includes $c$- and $g$-vectors, and show its compatibility with the unfolding. |
| title | Categorifications of Non-Integer Quivers: Types $H_4$, $H_3$ and $I_2(2n+1)$ |
| topic | Representation Theory Combinatorics Rings and Algebras 13F60 (Primary), 16G70, 16G20 (Secondary) |
| url | https://arxiv.org/abs/2204.12752 |