The coloured mutation class of $\mathbb{D}_n$- quivers and their application to $m$-cluster tilted algebras
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arXiv
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| Natura: | Preprint |
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2026
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| _version_ | 1866915956111966208 |
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| author | Gubitosi, Viviana Qureshi, Claudio |
| author_facet | Gubitosi, Viviana Qureshi, Claudio |
| contents | In this paper, we present an explicit and purely combinatorial characterization of the $m$-coloured quivers that appear within the $m$-coloured mutation class of a quiver of type $\mathbb{D}_n$. The $m$-coloured mutation, as defined by Buan and Thomas in \cite{BT}, generalises the well-known quiver mutation introduced by Fomin and Zelevinsky \cite{FZ}. Consequently, we derive a comprehensive description of the Gabriel quivers associated with $m$-cluster-tilted algebras of type $\mathbb{D}_n$. Notably, our characterization extends a result by Vatne, \cite{Va}, which we recover when $m=1$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_22972 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | The coloured mutation class of $\mathbb{D}_n$- quivers and their application to $m$-cluster tilted algebras Gubitosi, Viviana Qureshi, Claudio Representation Theory Combinatorics 13F60, 16G20, 05E15 In this paper, we present an explicit and purely combinatorial characterization of the $m$-coloured quivers that appear within the $m$-coloured mutation class of a quiver of type $\mathbb{D}_n$. The $m$-coloured mutation, as defined by Buan and Thomas in \cite{BT}, generalises the well-known quiver mutation introduced by Fomin and Zelevinsky \cite{FZ}. Consequently, we derive a comprehensive description of the Gabriel quivers associated with $m$-cluster-tilted algebras of type $\mathbb{D}_n$. Notably, our characterization extends a result by Vatne, \cite{Va}, which we recover when $m=1$. |
| title | The coloured mutation class of $\mathbb{D}_n$- quivers and their application to $m$-cluster tilted algebras |
| topic | Representation Theory Combinatorics 13F60, 16G20, 05E15 |
| url | https://arxiv.org/abs/2604.22972 |