论文标题
全量子交叉产品，不变措施和I型提升
Full quantum crossed products, invariant measures, and type-I lifting
论文作者
论文摘要
我们表明，对于封闭的嵌入$ \ mathbb {h} \ le \ mathbb {g} $的本地紧凑量量子组（LCQGS），带有$ \ mathbb {g}/\ mathbb {h} $ \ mathbb {h} $是。在相关说明的情况下，我们还证明，如果$ \ mathbb {g} \ Crocklearrowright在Unital $ c^*$上的LCQG $ a $ a $ c^*$ - 代数承认一个不变的状态，则$ \ \ \ \ m rathbb {g} $嵌入的整个crossed of Multerge note crossed and anger notbra notbra and and and ander note ander note anger note and and anger notbra notbra（and） Unital）。 我们还证明了越过LCQG动作的交叉产品的其他结果，其中一些似乎是民间传说。其中包括（a）两个相互双重量子组的形态产生同构完全交叉产物，以及（b）通过双辅助LCQGS完全和减少的交叉产物是同构的事实。
We show that for a closed embedding $\mathbb{H}\le \mathbb{G}$ of locally compact quantum groups (LCQGs) with $\mathbb{G}/\mathbb{H}$ admitting an invariant probability measure, a unitary $\mathbb{G}$-representation is type-I if its restriction to $\mathbb{H}$ is. On a related note, we also prove that if an action $\mathbb{G}\circlearrowright A$ of an LCQG on a unital $C^*$-algebra admits an invariant state then the full group algebra of $\mathbb{G}$ embeds into the resulting full crossed product (and into the multiplier algebra of that crossed product if the original algebra is not unital). We also prove a few other results on crossed products of LCQG actions, some of which seem to be folklore; among them are (a) the fact that two mutually dual quantum-group morphisms produce isomorphic full crossed products, and (b) the fact that full and reduced crossed products by dual-coamenable LCQGs are isomorphic.
