论文标题
在可正约和可凝结的坐骨上
On Amenable and Coamenable Coideals
论文作者
论文摘要
我们研究一个离散量子组的相对坐骨$ \ widetilde {n} _p \ subseteq \ subseteq \ ell^\ infty（\ mathbb {g}）$，就其类似群的投影而言。我们建立了一个$ p $ - 左不变状态的概念，并使用它来表征相对的舒适性。我们还提出了一个紧凑型准组$n_Ω\ subseteq l^\ infty（\ wideHat {\ mathbb {g}} $ subseteq l^\ subseteq l^\ subseteq l^\ subseteq l^\ subseteq l^} $的概念，该概念概括了由Kalantar，kalantar，kasprzak，selpalski和wery sheratients定义的商。 $ \ wideHat {\ mathbb {g}} $是$ \ mathbb {g} $的紧凑型双重。特别是，我们确定$ \ wideHat {\ mathbb {g}} $的可固定的紧凑型准书组是与$ c^*$ - 代数 - 代数 - 代数$ c_r（\ wideHat {\ mathbb {\ m mathbb {g}}）上的IDempotent态在一对一的对应。我们使用这项工作来获得划分性的二元性结果，并在$ \ ell^\ infty（\ Mathbb {g}）$中的二元性与它们在$ l^\ infty（\ wideHat {\ wideHat {\ mathbb {g}}}中的codual coideals的可依so胶的可依so;
We study relative amenability and amenability of a right coideal $\widetilde{N}_P\subseteq \ell^\infty(\mathbb{G})$ of a discrete quantum group in terms of its group-like projection $P$. We establish a notion of a $P$-left invariant state and use it to characterize relative amenability. We also develop a notion of coamenability of a compact quasi-subgroup $N_ω\subseteq L^\infty(\widehat{\mathbb{G}})$ that generalizes coamenability of a quotient as defined by Kalantar, Kasprzak, Skalski, and Vergnioux, where $\widehat{\mathbb{G}}$ is the compact dual of $\mathbb{G}$. In particular, we establish that the coamenable compact quasi-subgroups of $\widehat{\mathbb{G}}$ are in one-to-one correspondence with the idempotent states on the reduced $C^*$-algebra $C_r(\widehat{\mathbb{G}})$. We use this work to obtain results for the duality between relative amenability and amenability of coideals in $\ell^\infty(\mathbb{G})$ and coamenability of their codual coideals in $L^\infty(\widehat{\mathbb{G}})$, making progress towards a question of Kalantar et al{.}.
