Some prime factorization results for free quantum group factors
Some prime factorization results for free quantum group factors
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DOI：
10.1515/crelle-2014-0056
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发表时间：
2014-01
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影响因子：
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通讯作者：
Yusuke Isono
中科院分区：
文献类型：
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作者：
Yusuke Isono
证明了自由量子群因子张量积的一些独特的分解结果。它们是Ozawa和Popa建立的双精确群的直接产物分解结果的III型类似物。在证明中，我们首先取张量积的连续核，它满足一个类似于条件（AO）的条件，并讨论了连续核的一些分解性质。然后我们推导出原始III型因子的分解性质。我们还用双精确群的直接积证明了交叉积von Neumann代数的一些唯一的分解结果。
We prove some unique factorization results for tensor products of free quantum group factors. They are type III analogues of factorization results for direct products of bi-exact groups established by Ozawa and Popa. In the proof, we first take continuous cores of the tensor products, which satisfy a condition similar to condition (AO), and discuss some factorization properties for the continuous cores. We then deduce factorization properties for the original type III factors. We also prove some unique factorization results for crossed product von Neumann algebras by direct products of bi-exact groups.