Fractional Brauer configuration algebras II: covering theory
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866917430598565888 |
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| author | Li, Nengqun Liu, Yuming |
| author_facet | Li, Nengqun Liu, Yuming |
| contents | In this paper, we develop a covering theory for the fractional Brauer configurations and connect it with the coverings of the associated quivers with relations in the sense of Martínez-Villa and de la Peña. Among the results, we show the following: (1) The universal cover of any fractional Brauer configuration is simply connected and we construct explicitly the universal cover of fractional Brauer configurations of type MS; (2) The fundamental group of a fractional Brauer configuration $E$ of type S is isomorphic to the fundamental group of the associated quiver with relations $(Q_E,I_E)$; (3) A (regular) covering of fractional Brauer configurations induces a (Galois) covering of the associated fractional Brauer configuration categories; (4) Set up an analogy of Van Kampen theorem for fractional Brauer configurations and apply it to calculate the fundamental group of any connected Brauer configuration. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2412_13445 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Fractional Brauer configuration algebras II: covering theory Li, Nengqun Liu, Yuming Representation Theory 16Gxx, 16B50 In this paper, we develop a covering theory for the fractional Brauer configurations and connect it with the coverings of the associated quivers with relations in the sense of Martínez-Villa and de la Peña. Among the results, we show the following: (1) The universal cover of any fractional Brauer configuration is simply connected and we construct explicitly the universal cover of fractional Brauer configurations of type MS; (2) The fundamental group of a fractional Brauer configuration $E$ of type S is isomorphic to the fundamental group of the associated quiver with relations $(Q_E,I_E)$; (3) A (regular) covering of fractional Brauer configurations induces a (Galois) covering of the associated fractional Brauer configuration categories; (4) Set up an analogy of Van Kampen theorem for fractional Brauer configurations and apply it to calculate the fundamental group of any connected Brauer configuration. |
| title | Fractional Brauer configuration algebras II: covering theory |
| topic | Representation Theory 16Gxx, 16B50 |
| url | https://arxiv.org/abs/2412.13445 |