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arXiv · 1807.04470

On Burnside Theory for groupoids

Laiachi El Kaoutit·Leonardo Spinosa
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Abstract

We explore the concept of conjugation between subgroupoids, providing several characterizations of the conjugacy relation (Theorem A in {\S}1.2). We show that two finite groupoid-sets, over a locally strongly finite groupoid, are isomorphic, if and only if, they have the same number of fixed points with respect to any subgroupoid with a single object (Theorem B in {\S}1.2). Lastly, we examine the ghost map of a finite groupoid and the idempotents elements of its Burnside algebra. The exposition includes an Appendix where we gather the main general technical notions that are needed along the paper.

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Laiachi El Kaoutit, Leonardo Spinosa. 2018-07-12. On Burnside Theory for groupoids. https://arxiv.org/abs/1807.04470

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