Maximal von Neumann subalgebras arising from maximal subgroups  

作　　者：Yongle Jiang 

机构地区：[1]School of Mathematical Sciences,Dalian University of Technology,Dalian 116024,China

出　　处：《Science China Mathematics》2021年第10期2295-2312,共18页中国科学：数学（英文版）

基　　金：the National Science Center(NCN)(Grant No.2014/14/E/ST1/00525);Institute of Mathematics,Polish Academy of Sciences(IMPAN)from the Simons Foundation(Grant No.346300);the Matching 2015-2019 Polish Ministry of Science and Higher Education(MNiSW)Fund,and the Research Foundation-Flanders-Polish Academy of Sciences(FWO-PAN).

摘　　要：Ge(2003)asked the question whether LF∞can be embedded into LF2 as a maximal subfactor.We answer it affirmatively with three different approaches,all containing the same key ingredient:the existence of maximal subgroups with infinite index.We also show that point stabilizer subgroups for every faithful,4-transitive action on an infinite set give rise to maximal von Neumann subalgebras.By combining this with the known results on constructing faithful,highly transitive actions,we get many maximal von Neumann subalgebras arising from maximal subgroups with infinite index.

关 键 词：maximal von Neumann subalgebra maximal subfactor maximal subgroup highly transitive action rigid subalgebra 

分 类 号：O15[理学—数学]