论文标题
在横断产品的统一组上
On unitary groups of crossed product von Neumann algebras
论文作者
论文摘要
我们考虑奇特的跨产品代数$ m = a \rtimesλ$是由痕量保存动作$σ产生的：λ\ curvearrowright在tracial von neumann elgebra $ a $ a $ a $ a $ a $ a $ a $ a $ a $ a $ a $ a $ a $ a $ a $ a $ a $ a $ a $。对于统一的子组$ \ Mathcal {g} \ subset \ Mathcal {u}（m）$，我们研究了$ \ MATHCAL {G} $可以将其连接到$ \ Mathcal {u}（a）\cdotλ$ in $ m $中。我们为此提供了充分的条件。我们的结果概括了ioana，popa和vaes的结果，当$ m $是von neumann代数$ l（λ）$时，它们会对待情况。
We consider the tracial crossed product algebra $M=A\rtimesΛ$ arising from a trace preserving action $σ:Λ\curvearrowright A$ of a discrete group $Λ$ on a tracial von Neumann algebra $A$. For a unitary subgroup $\mathcal{G}\subset \mathcal{U}(M)$, we study when this $\mathcal{G}$ can be conjugated into $\mathcal{U}(A)\cdotΛ$ in $M$. We provide a general sufficient condition for this to happen. Our result generalizes a result of Ioana, Popa and Vaes, which treats the case when $M$ is the group von Neumann algebra $L(Λ)$.
