Fractional Brauer configuration algebras II: covering theory

2024/12/18 by Nengqun Li, Yuming Liu, Li, Nengqun +1 · 1 citation
Mathematics · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.2412.13445

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 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.

Cited by

• A lecture note on covering theory in representation theory of algebras

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