Nakajima's quiver varieties and triangular bases of bipartite cluster algebras
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866914795725258752 |
|---|---|
| author | Li, Li |
| author_facet | Li, Li |
| contents | Berenstein and Zelevinsky introduced quantum cluster algebras \cite{BZ1} and the triangular bases \cite{BZ2}. The support conjecture proposed in \cite{LLRZ}, which asserts that the support of each triangular basis element for a rank-2 cluster algebra is bounded by an explicitly described region, was established in \cite{L} for skew-symmetric rank-2 cluster algebras. In this paper we extend this result by proving a bound on the support of each triangular basis element for bipartite cluster algebras. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_08234 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Nakajima's quiver varieties and triangular bases of bipartite cluster algebras Li, Li Representation Theory Algebraic Geometry Primary 13F60, Secondary 14F06, 16G20, 32S60 Berenstein and Zelevinsky introduced quantum cluster algebras \cite{BZ1} and the triangular bases \cite{BZ2}. The support conjecture proposed in \cite{LLRZ}, which asserts that the support of each triangular basis element for a rank-2 cluster algebra is bounded by an explicitly described region, was established in \cite{L} for skew-symmetric rank-2 cluster algebras. In this paper we extend this result by proving a bound on the support of each triangular basis element for bipartite cluster algebras. |
| title | Nakajima's quiver varieties and triangular bases of bipartite cluster algebras |
| topic | Representation Theory Algebraic Geometry Primary 13F60, Secondary 14F06, 16G20, 32S60 |
| url | https://arxiv.org/abs/2405.08234 |