Invariant sets and normal subgroupoids of universal étale groupoids induced by congruences of inverse semigroups

Isomorphism Theorems for Groupoids and Some Applications

Using an algebraic point of view we present an introduction to the groupoid theory, that is, we give fundamental properties of groupoids as, uniqueness of inverses and properties of the identities, and study subgroupoids, wide subgroupoids and normal subgroupoids. We also present the isomorphism theorems for groupoids and as an applications we obtain the corresponding version of Zassenhaus Lemma and Jordan-Hölder Theorem for groupoids. Finally inspired by the Ehresmann-Schein-Nambooripad Theorem we improve a result of R. Exel concerning a one to one correspondence between partial actions of gr…

A correspondence between inverse subsemigroups, open wide subgroupoids and Cartan intermediate C*-subalgebras

For a given inverse semigroup action on a topological space, one can associate an étale groupoid. We prove that there exists a correspondence between the certain subsemigroups and the open wide subgroupoids in case that the action is strongly tight. Combining with the recent result of Brown et. al, we obtain a correspondence between the certain subsemigroups of an inverse semigroup and the Cartan intermediate subalgebras of a groupoid C*-algebra.

On normal subgroupoids

In this paper we present some algebraic properties of subgroupoids and normal subgroupoids. We define the normalizer of a wide subgroupoid $\mathcal{H}$ and show that, as in the case of groups, the normalizer is the greatest wide subgroupoid of the groupoid $\mathcal{G}$ in which $\mathcal{H}$ is normal. Furthermore, we give the definition of center and commutator and prove that both are normal subgroupoids, the first one of the union of all the isotropy groups of $\mathcal{G}$ and the second one of $\mathcal{G}$. Finally, we introduce the concept of inner isomorphism of $\mathcal{G}$ and show…

A Package of Programs for Determination of Some Classes of Subgroupoids

We give three programs on computer for finding the subgroupoids, wide subgroupoids and normal subgroupoids of a finite groupoid.

有限型移位的拓扑全群的极大子群

Maximal subgroups of topological full groups of shifts of finite type

该研究探讨有限型移位拓扑全群的极大子群，证明素子群胚的三分性，给出其拓扑全群正规化子为极大的判据，扩展Thompson群V相关结果并得到含交换子群的子群的极大子群数量结论。

On Burnside Theory for groupoids

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.