离散群与量子自同构群的自由圈积
The free wreath product of a discrete group by a quantum automorphism group
摘要：
设$\mathbb{G}$是有限维C*-代数$(B,ψ)$的量子自同构群，$Γ$是离散群.我们要计算$\widehatΓ\wr_* \mathbb{G}$的融合规则。首先，我们将修改$\mathbb{G}$的表示论，特别是，我们将使用非交叉划分来描述交织空间。它将使我们能够找到在一般情况下的状态$ψ$的自由圈积的融合规则。当$ψ$是迹时，证明了约化C*-代数的简单性;当$Γ$是有限迹时，证明了$L^\infty(\widehatΓ\wr_* \mathbb{G})$的Haagerup性质.
英文摘要：
Let $\mathbb{G}$ be the quantum automorphism group of a finite dimensional C*-algebra $(B,ψ)$ and $Γ$ a discrete group. We want to compute the fusion rules of $\widehatΓ\wr_* \mathbb{G}$. First of all, we will revise the representation theory of $\mathbb{G}$ and, in particular, we will describe the spaces of intertwiners by using noncrossing partitions. It will allow us to find the fusion rules of the free wreath product in the general case of a state $ψ$. We will also prove the simplicity of the reduced C*-algebra, when $ψ$ is a trace, as well as the Haagerup property of $L^\infty(\widehatΓ\wr_* \mathbb{G})$, when $Γ$ is moreover finite.
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