Strongly Solid II1 Factors with an Exotic MASA
Strongly Solid II1 Factors with an Exotic MASA
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具有异国情调的 MASA 的坚固 II1 因子
DOI：
10.1093/imrn/rnq117
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发表时间：
2010
影响因子：
1
通讯作者：
D. Shlyakhtenko
中科院分区：
文献类型：
--
作者：
Cyril Houdayer;D. Shlyakhtenko
利用Ozawa和Popa技巧的推广，我们给出了一个非顺从强实II 1因子M包含一个“奇异”极大交换子代数A的例子：作为A，A-双模，L2（M）既不粗糙也不离散.因此，我们证明了存在具有这种性质的II 1因子，但不存在Cartan子代数.它也遵循Voiculescu的自由熵的结果，M是不是一个内插的自由群因子，但它是强固体，并具有Haagerup属性和完全度量近似属性。
Using an extension of techniques of Ozawa and Popa, we give an example of a non-amenable strongly solid II 1 factor M containing an “exotic” maximal abelian subalgebra A: as an A,A-bimodule, L 2 (M) is neither coarse nor discrete. Thus, we show that there exist II 1 factors with such property but without Cartan subalgebras. It also follows from Voiculescu's free entropy results that M is not an interpolated free group factor, yet it is strongly solid and has both the Haagerup property and the complete metric approximation property.