AI 中文总结
本文引入有向二元辫群，统一了辫群与定向Thompson群的Jones表示，并构造了扩展的酉表示及嵌入，使辫闭包恢复定向链环构造。
AI 中文摘要
我们通过引入有向二元辫群来统一辫群和定向Thompson群的Jones表示。这个有限生成群包含所有辫群和定向Thompson群。我们构造了定向Thompson群到该群的嵌入，使得取辫闭包可恢复Jones对定向链环的构造。我们还引入了二元Temperley-Lieb代数，并构造了有向二元辫群的酉表示，该表示扩展了辫群的经典Jones表示。沿Thompson群的嵌入，其显著矩阵系数与定向Thompson群的Jones表示的相应系数一致。
英文摘要
We unify Jones' representations of braid groups and the oriented Thompson's group by introducing the oriented dyadic braid group. This finitely generated group contains every braid group and the oriented Thompson's group. We construct an embedding of the oriented Thompson's group into this group such that taking braid closures recovers Jones' construction of oriented links. We also introduce the dyadic Temperley-Lieb algebra and construct a unitary representation of the oriented dyadic braid group extending the classical Jones representations of braid groups. Along the Thompson group's embedding, its distinguished matrix coefficient agrees with the corresponding coefficient of Jones' representation of the oriented Thompson's group.
Comments32 pages, 18 figures
