On Burnside Theory for groupoids

被引：0
|
作者：
El Kaouttt, Laiachi [1 ,2 ]
Spinosa, Leonardo [3 ]
机构：
[1] Univ Granada, Dept Algebra, Fuente Nueva s-n, E-18071 Granada, Spain
[2] Univ Granada, IMAG, Fac Ciencias, Fuente Nueva s-n, E-18071 Granada, Spain
[3] Univ Ferrara, Dept Math & Comp Sci, Via Machiavelli 30, I-44121 Ferrara, Italy
来源：
BULLETIN MATHEMATIQUE DE LA SOCIETE DES SCIENCES MATHEMATIQUES DE ROUMANIE | 2023年 / 66卷 / 01期
关键词：
The monoidal category of groupoid-bisets; conjugation between sub-groupoids; Burnside Theorem; Burnside ring of finite groupoids; table of marks; the ghost map and the idempotents; Laplaza categories; CATEGORIES; RINGS;
D O I：
暂无
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We explore the concept of conjugation between subgroupoids, providing several characterizations of the conjugacy relation (Theorem A in 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 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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页码：41 / 87
页数：47
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