Haagerup approximation property via bimodules
Haagerup approximation property via bimodules
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DOI：
10.7146/math.scand.a-25970
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发表时间：
2015-01
期刊：
影响因子：
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通讯作者：
Rui Okayasu;N. Ozawa;Reiji Tomatsu
中科院分区：
文献类型：
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作者：
Rui Okayasu;N. Ozawa;Reiji Tomatsu
定义了有限von Neumann代数的Haagerup逼近性质（HAP），使得离散群的群von Neumann代数具有HAP当且仅当群本身具有Haagerup性质. HAP在有限von Neumann代数上得到了广泛的研究，最近Caspers-Skalski和Okayasu-Tomatsu将其推广到任意von Neumann代数上。推广背后的动机之一是量子群冯诺依曼代数通常是无限的，即使Daws-Fima-Skalski-White已经成功地定义了局部紧量子群的Haagerup性质。本文通过证明具有Haagerup性质的局部紧量子群的von Neumann代数具有HAP，部分地填补了这一空白。即使对于真正的地方紧密群体来说，这也是新的。
The Haagerup approximation property (HAP) is defined for finite von Neumann algebras in such a way that the group von Neumann algebra of a discrete group has the HAP if and only if the group itself has the Haagerup property. The HAP has been studied extensively for finite von Neumann algebras and it is recently generalized for arbitrary von Neumann algebras by Caspers-Skalski and Okayasu-Tomatsu. One of the motivations behind the generalization is the fact that quantum group von Neumann algebras are often infinite even though the Haagerup property has been defined successfully for locally compact quantum groups by Daws-Fima-Skalski-White. In this paper, we partly fill this gap by proving that the von Neumann algebra of a locally compact quantum group with the Haagerup property has the HAP. This is new even for genuine locally compact groups.