Continuous Quivers of Type A (III) Embeddings of Cluster Theories
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arXiv
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| Format: | Preprint |
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2020
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| _version_ | 1866916797923459072 |
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| author | Igusa, Kiyoshi Rock, Job D. Todorov, Gordana |
| author_facet | Igusa, Kiyoshi Rock, Job D. Todorov, Gordana |
| contents | We continue the work started in parts (I) and (II). In this part we classify which continuous type A quivers are derived equivalent and introduce the new continuous cluster category with E-clusters, which are a generalization of clusters. In the middle we provide a rigorous connection between the previous construction of the continuous cluster category and the new construction. We conclude with the introduction of a cluster theory, generalizing the notion of a cluster structure. Using this new notion, we demonstrate how one embeds known type A cluster theories into the new E-cluster theory in a way compatible with mutation. This is part (III) in a series of work that will conclude with a continuous generalization of mutation for cluster theories. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2004_10740 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Continuous Quivers of Type A (III) Embeddings of Cluster Theories Igusa, Kiyoshi Rock, Job D. Todorov, Gordana Representation Theory Category Theory Primary: 13F60, Secondary: 16G20 We continue the work started in parts (I) and (II). In this part we classify which continuous type A quivers are derived equivalent and introduce the new continuous cluster category with E-clusters, which are a generalization of clusters. In the middle we provide a rigorous connection between the previous construction of the continuous cluster category and the new construction. We conclude with the introduction of a cluster theory, generalizing the notion of a cluster structure. Using this new notion, we demonstrate how one embeds known type A cluster theories into the new E-cluster theory in a way compatible with mutation. This is part (III) in a series of work that will conclude with a continuous generalization of mutation for cluster theories. |
| title | Continuous Quivers of Type A (III) Embeddings of Cluster Theories |
| topic | Representation Theory Category Theory Primary: 13F60, Secondary: 16G20 |
| url | https://arxiv.org/abs/2004.10740 |