大型阿尔丁群的特征

IF 0.8 3区数学 Q2 MATHEMATICS Bulletin of the London Mathematical Society Pub Date : 2024-08-19 DOI:10.1112/blms.13136

Alexandre Martin, Nicolas Vaskou

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引用次数: 0

摘要

我们证明了大类型阿汀群类在同构下是不变的，这与考斯特群的相应情况形成了鲜明对比。我们通过提供大型阿尔丁群的纯代数特征（即与呈现图无关）来获得这一结果。作为推论，我们完全描述了与给定大型阿汀群同构的阿汀群，并描述了那些刚性大型阿汀群的特征。

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Characterising large-type Artin groups

We show that the class of large-type Artin groups is invariant under isomorphism, in stark contrast with the corresponding situation for Coxeter groups. We obtain this result by providing a purely algebraic characterisation of large-type Artin groups (i.e. independent of the presentation graph). As a corollary, we completely describe the Artin groups isomorphic to a given large-type Artin group, and characterise those large-type Artin groups that are rigid.

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