Structure of II1 factors arising from free Bogoljubov actions of arbitrary groups
Structure of II1 factors arising from free Bogoljubov actions of arbitrary groups
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任意群的自由 Bogoljubov 作用产生的 II1 因子的结构
DOI：
10.1016/j.aim.2014.04.010
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发表时间：
2012
影响因子：
1.7
通讯作者：
Cyril Houdayer
中科院分区：
文献类型：
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作者：
Cyril Houdayer
本文研究了任意可数离散群的正交表示π：G→ O（HR）的自由Bogoljubov作用所产生的交叉积II1因子M的几个结构性质.在相当一般的正交表示π：G→ O（HR）的假设下，我们证明了M不具有Murray和von Neumann的Gamma性质.证明了任意正则顺从子代数A ∈ M都可以嵌入到L（G）中M的内部.最后，当G被假定为顺从时，我们精确地定位了L（G）在M内的任何可能的顺从或Gamma扩张。
In this paper, we investigate several structural properties for crossed product II 1 factors M arising from free Bogoljubov actions associated with orthogonal representations π: G→ O (H R) of arbitrary countable discrete groups. Under fairly general assumptions on the orthogonal representation π: G→ O (H R), we show that M does not have property Gamma of Murray and von Neumann. Then we show that any regular amenable subalgebra A⊂ M can be embedded into L (G) inside M. Finally, when G is assumed to be amenable, we locate precisely any possible amenable or Gamma extension of L (G) inside M.