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Dynamical systems and operator algebras associated to Artin's representation of braid groups. (arXiv:1609.04737v2 [math.OA] UPDATED)
来源于:arXiv
Artin's representation is an injective homomorphism from the braid group
$B_n$ on $n$ strands into $\operatorname{Aut}\mathbb{F}_n$, the automorphism
group of the free group $\mathbb{F}_n$ on $n$ generators. The representation
induces maps $B_n\to\operatorname{Aut}C^*_r(\mathbb{F}_n)$ and
$B_n\to\operatorname{Aut}C^*(\mathbb{F}_n)$ into the automorphism groups of the
corresponding group $C^*$-algebras of $\mathbb{F}_n$. These maps also have
natural restrictions to the pure braid group $P_n$. In this paper, we consider
twisted versions of the actions by cocycles with values in the circle, and
discuss the ideal structure of the associated crossed products. Additionally,
we make use of Artin's representation to show that the braid groups $B_\infty$
and $P_\infty$ on infinitely many strands are both $C^*$-simple. 查看全文>>