Fractional Brauer configuration algebras II: covering theory

Nengqun Li; Yuming Liu

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arXiv · 2412.13445

Fractional Brauer configuration algebras II: covering theory

Nengqun Li·Yuming Liu

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Abstract

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 Mart\'inez-Villa and de la Pe\~na. 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.

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BibTeX RIS

Nengqun Li, Yuming Liu. 2024-12-18. Fractional Brauer configuration algebras II: covering theory. https://arxiv.org/abs/2412.13445

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