标题： 不变子代数对von Neumann代数的刚性，这些代数来自某些半直积群 显示英文标题

标题： Invariant subalgebras rigidity for von Neumann algebras of groups arising as certain semidirect products

摘要： 我们研究某些离散群的ISR（冯·诺依曼不变子代数刚性）性质，这些群作为代数作用在某些2-挠群上的半直积而出现，大部分作为直接积的$\mathbb{Z}_2$出现。 我们特别给出了第一个具有ISR性质的可解群的例子，该群包含一个非平凡的阿贝尔正规子群。 讨论了其他几个例子，特别是包括一个无限可解群，其冯·诺依曼代数恰好只有一个不变的冯·诺依曼子代数，该子代数并非来自正规子群。 我们还研究了标准灯夫群的群冯·诺依曼代数的不变子代数的形式。 显示英文摘要

摘要： We study the ISR (von Neumann invariant subalgebra rigidity) property for certain discrete groups arising as semidirect products from algebraic actions on certain 2-torsion groups, mostly arising as direct products of $\mathbb{Z}_2$. We present, in particular, the first example of an amenable group with the ISR property that admits a non-trivial abelian normal subgroup. Several other examples are discussed, notably including an infinite amenable group whose von Neumann algebra admits precisely one invariant von Neumann subalgebra which does not come from a normal subgroup. We also investigate the form of invariant subalgebras of the group von Neumann algebra of the standard lamplighter group.