arXiv subjects

João V. P. e Silva

Publications and source records attributed to João V. P. e Silva.

3 recordsLinked to original sources

arXiv2025

Topological incidence rings and the incidence functors

We focus on working on incidence rings, a class of (possibly infinite) matrix rings indexed by ordered sets. Some general properties about them are given, including how they are always the inverse limit of finite matrix rings, giving a natural way to define their topology. We then show that such construction can be translated as a functor from the category of locally finite, preordered sets to the category of (topological) incidence rings that maps colimits to limits. We also shortly discuss the consequences of these results to the class of groups of units of incidence rings, as the unit functor allow us to translate most of the results.

math.GR↗

arXiv2024

Topologically simple infinite matrix groups indexed by ordered sets

This article focuses on the study of the group of units of incidence rings, which is a class of infinite matrix groups indexed by ordered sets, on a topological perspective. We first show when these groups can inherit the topological structure from the incidence rings. It is later shown that infinite matrix groups of topological fields can be used to build simple topological matrix groups, generalizing a result proven in ``Topologically simple, totally disconnected, locally compact infinite matrix groups''. We finish by relating the structure of these groups with elementary totally disconnected, locally compact groups, an important class for the study of totally disconnected, locally compact groups.

math.GR↗

arXiv2023

Elementary totally disconnected, locally compact groups of higher complexity

The article focuses on a class of second countable groups assembled from profinite and discrete by elementary operations. We focus on a rank associated with these groups that measure their complexity, the decomposition rank. A collection of groups acting on $\aleph_0$-regular trees is defined and used for the first construction of a group with decomposition rank $ω^ω+1$.

math.GR↗