Finite Fields and Their Applications ( IF 1.2 ) Pub Date : 2020-07-13 , DOI: 10.1016/j.ffa.2020.101706 J. D'haeseleer , J. Mannaert , L. Storme , A. Švob
The study of Cameron-Liebler line classes in PG() arose from classifying specific collineation subgroups of PG(). 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(). 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(). Next to giving this link, we will also give some equivalent ways to consider Cameron-Liebler line classes in AG(), some classification results and an example based on the example found in [3] and [6].
中文翻译:
AG(3,q)中的Cameron-Liebler线类
PG中Cameron-Liebler线类的研究)来自对PG()的特定归类子组进行分类)。最近,在新设置中考虑了这些线路类。因此,我们将Cameron-Liebler线类的概念推广到AG()。在本文中,我们使用线交的常数交集属性定义Cameron-Liebler线类。关于这种概括的有趣事实是,这些线类与PG中的Cameron-Liebler线类具有联系()。除了提供此链接外,我们还将提供一些等效的方法来考虑AG()中的Cameron-Liebler线类),一些分类结果和一个基于[3]和[6]中的示例的示例。