论文标题
量子相对模块化函数
Quantum relative modular functions
论文作者
论文摘要
令$ \ mathbb {h} \ trianglelefteq \ mathbb {g} $是本地紧凑型量子组的封闭正常子组。我们介绍了一个严格的积极群体状元素，该元素与$ l^{\ infty}（\ Mathbb {g}）$相关，该元素大致衡量了$ \ mathbb {g} $的失败，以通过conjugation conjugation对$ \ mathbb {h} $进行$ \ mathbb {h} $。该元素的琐碎性等同于$ \ mathbb {g} $和$ \ mathbb {g}/\ mathbb {h} $具有相同的模块化元素，与经典情况相比具有相同的模块化元素。如果$ \ mathbb {h} \ le \ mathbb {g} $是中心的，则此条件是自动的，并且通常意味着$ \ mathbb {h h} $的单模型。 我们还描述了与$ C_0（\ Mathbb {G}）$相关的严格积极群体元素$Δ$之间的两次循环培养，量子群形态$ \ Mathbb {g} \ to（\ Mathbb {r}，+）$，在$Δ$ $Δ$之间易于封闭形象，并在封闭的形象中易于描述。然后，这意味着属性 - （t）局部紧凑的量子群未承认非明显的严格构成群体样元素。
Let $\mathbb{H}\trianglelefteq\mathbb{G}$ be a closed normal subgroup of a locally compact quantum group. We introduce a strictly positive group-like element affiliated with $L^{\infty}(\mathbb{G})$ that, roughly, measures the failure of $\mathbb{G}$ to act measure-preservingly on $\mathbb{H}$ by conjugation. The triviality of that element is equivalent to the condition that $\mathbb{G}$ and $\mathbb{G}/\mathbb{H}$ have the same modular element, by analogy with the classical situation. This condition is automatic if $\mathbb{H}\le \mathbb{G}$ is central, and in general implies the unimodularity of $\mathbb{H}$. We also describe a bijection between strictly positive group-like elements $δ$ affiliated with $C_0(\mathbb{G})$ and quantum-group morphisms $\mathbb{G}\to (\mathbb{R},+)$, with the closed image of the morphism easily described in terms of the spectrum of $δ$. This then implies that property-(T) locally compact quantum groups admit no non-obvious strictly positive group-like elements.
