Actions of _{∞} whose II₁ factors and orbit equivalence relations have prescribed fundamental group
Actions of _{∞} whose II₁ factors and orbit equivalence relations have prescribed fundamental group
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II₁因子和轨道等价关系规定基本群的_{∞}的作用
DOI：
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发表时间：
2008
期刊：
影响因子：
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通讯作者：
S. Vaes
中科院分区：
文献类型：
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作者：
S. Popa;S. Vaes
We show that given any subgroup F of R+ which is either countable or belongs to a certain “large” class of uncountable subgroups, there exist continuously many free ergodic measure preserving actions i of the free group with infinitely many generators F1 on probability measure spaces (Xi,µi) such that their associated group measure space II1 factors Mi = L 1 (Xi)o i F1 and orbit equivalence relationsRi =R(F1 y Xi) have fundamental group equal toF and with Mi (respectivelyRi) stably non-isomorphic. Moreover, these actions can be taken so thatRi has no outer automorphisms and any automorphism of Mi is unitary conjugate to an automorphism that acts trivially on the subalgebra L 1 (Xi) of Mi.
