论文标题
虚拟图产品中的共轭语言
Conjugacy languages in virtual graph products
论文作者
论文摘要
在本文中，我们研究了虚拟图产品中共轭语言的行为，从而扩展了Ciobanu，Hermiller，Holt和Rees的结果。我们主要关注半独立产品的虚拟图产品。首先，我们研究了右角Artin和Coxeter组中扭曲的共轭代表的行为。在某些情况下，我们证明了虚拟图产品的共轭测量语言的规律性，并突出了球形共轭语言的属性，具体取决于自动形态和在生成集上的订购。最后，我们给出一个标准，即何时球形共轭语言对于虚拟图产品而言并非明确的上下文。在虚拟Raags的情况下，我们可以进一步扩展这一点，以表明球形共轭语言并非没有上下文。
In this paper we study the behaviour of conjugacy languages in virtual graph products, extending results by Ciobanu, Hermiller, Holt and Rees. We focus primarily on virtual graph products in the form of a semi-direct product. First, we study the behaviour of twisted conjugacy representatives in right-angled Artin and Coxeter groups. We prove regularity of the conjugacy geodesic language for virtual graph products in certain cases, and highlight properties of the spherical conjugacy language, depending on the automorphism and ordering on the generating set. Finally, we give a criterion for when the spherical conjugacy language is not unambiguous context-free for virtual graph products. We can extend this further in the case of virtual RAAGs, to show the spherical conjugacy language is not context-free.
