Cameron-Liebler line classes in AG(3,q)

The study of Cameron-Liebler line classes in PG(\(3,q\)) arose from classifying specific collineation subgroups of PG(\(3,q\)). Recently, these line classes were considered in new settings. In this point of view, we will generalize the concept of Cameron-Liebler line classes to AG(\(3,q\)). In this...

Full description

Saved in:
Bibliographic Details
Published in:arXiv.org 2021-03
Main Authors: D'haeseleer, Jozefien, Mannaert, Jonathan, Storme, Leo, Svob, Andrea
Format: Article
Language:English
Subjects:
Classification
Subgroups
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:The study of Cameron-Liebler line classes in PG(\(3,q\)) arose from classifying specific collineation subgroups of PG(\(3,q\)). Recently, these line classes were considered in new settings. In this point of view, we will generalize the concept of Cameron-Liebler line classes to AG(\(3,q\)). In this article we define Cameron-Liebler line classes using the constant intersection property towards line spreads. The interesting fact about this generalization is the link these line classes have with Cameron-Liebler line classes in PG(\(3,q\)). Next to giving this link, we will also give some equivalent ways to consider Cameron-Liebler line classes in AG(\(3,q\)), some classification results and an example based on the example found in [3] and [6].
ISSN:2331-8422
DOI:10.48550/arxiv.2002.02700