论文标题
由琼斯技术产生的汤普森相关群体的分类I
Classification of Thompson related groups arising from Jones technology I
论文作者
论文摘要
在构建保形领域理论（CFT）的追求中，琼斯发现了CFT，Richard Thompson的群体和结理论之间的美丽而深厚的联系。这导致了一个强大的功能框架，用于构建由汤普森（Thompson）组和辫子组等类别引起的特定群体的行动。特别是，给定一个组及其两个内态性，可以在最大的汤普森（Thompson）的$ v $表现中构建半程产品。这些半领产品具有显着的图形描述，以前用来提供具有Haagerup属性的组的新示例。它们自然出现在某些领域理论中，是由本地和全球对称性产生的。此外，这些群体发生在Tanushevski的构造中，可以使用Witzel-Zaremsky克隆系统的技术使用Brin-Zappa-Szep的产品实现。 我们在本文中考虑了以这种方式获得的一类，其中一个内态性是微不足道的，将两个非平凡的内态性的情况放在第二篇文章中。我们将所有这些群体的明确描述作为排列限制的扭曲的花圈产品，其中$ v $是组的表演，扭曲取决于所选择的内态性。由于意外的刚性现象，我们将这类群体分类为同构，并对其自身形态群体进行稀薄的描述。
In the quest in constructing conformal field theories (CFT) Jones has discovered a beautiful and deep connection between CFT, Richard Thompson's groups and knot theory. This led to a powerful functorial framework for constructing actions of particular groups arising from categories such as Thompson's groups and braid groups. In particular, given a group and two of its endomorphisms one can construct a semidirect product where the largest Thompson's group $V$ is acting. These semidirect products have remarkable diagrammatic descriptions which were previously used to provide new examples of groups having the Haagerup property. They naturally appear in certain field theories as being generated by local and global symmetries. Moreover, these groups occur in a construction of Tanushevski and can be realised using Brin-Zappa-Szep's products with the technology of cloning systems of Witzel-Zaremsky. We consider in this article the class of groups obtained in that way where one of the endomorphism is trivial leaving the case of two nontrivial endomorphisms to a second article. We provide an explicit description of all these groups as permutational restricted twisted wreath products where $V$ is the group acting and the twist depends on the endomorphism chosen. We classify this class of groups up to isomorphisms and provide a thin description of their automorphism group thanks to an unexpected rigidity phenomena.
