论文标题
圆环结组和一些复杂的辫子组上的一个新的Garside结构
A new Garside structure on torus knot groups and some complex braid groups
论文作者
论文摘要
已知有几个不同的GARSIDE小脚体，它们是圆环基组作为馏分组。对于$ n，m \ geq 2 $两个coprime整数，我们引入了一个新的Garside Monoid $ \ Mathcal {m}（M}（n，m）$，As Garside Group as Garside Group $（n，m）$ - torus nong group，从而推广到所有Torus knot groups，我们以前为$（N，N，N+1）$ 1）$ torus Knot组提供了一个结构。作为副产品，我们为少数等级第二等级的复杂反射组的编织组获得了新的Garside结构。还为其他几个额外的辫子组构建了类似的Garside结构，该组由$ g_ {13} $和偶数类型的二二二邻artin组组成，这些等级第二等级的等级第二等级式反射群。
Several distinct Garside monoids having torus knot groups as groups of fractions are known. For $n,m\geq 2$ two coprime integers, we introduce a new Garside monoid $\mathcal{M}(n,m)$ having as Garside group the $(n,m)$-torus knot group, thereby generalizing to all torus knot groups a construction that we previously gave for the $(n,n+1)$-torus knot group. As a byproduct, we obtain new Garside structures for the braid groups of a few exceptional complex reflection groups of rank two. Analogous Garside structures are also constructed for a few additional braid groups of exceptional complex reflection groups of rank two which are not isomorphic to torus knot groups, namely for $G_{13}$ and for dihedral Artin groups of even type.
