冯·诺依曼代数交叉积的一点注记 |
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引用本文: | 吴文明,袁巍.冯·诺依曼代数交叉积的一点注记[J].数学学报,2008,51(4):803-808. |
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作者姓名: | 吴文明 袁巍 |
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作者单位: | 清华大学数学科学系,中国科学院数学与系统科学研究院 北京 100084 重庆师范大学数学与计算机学院 重庆 400047,北京 100080 |
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摘 要: | 设α是可数离散群G和H的半直积G■_σH在冯·诺依曼代数M上的作用,则β_h=α_((e,h))AdU_h定义了群H在冯·诺依曼代数交叉积M■_αG上的作用β.本文证明了交叉积冯·诺依曼代数M■_α(G■_σH)与(M■_αG)■_βH是*-同构的,因此在一定条件下,冯·诺依曼代数的交叉积满足结合律.
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关 键 词: | 半直积 可数离散群 交叉积 冯·诺依曼代数 |
收稿时间: | 2007-4-29 |
A Note on the Crossed Product of von Neumann Algebras |
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Institution: | Wen Ming WU Department of Mathematical Science,Tsinghua University,Beijing 100084,P.R.China College of Mathematics & Computer Science,Chongqing Normal University,Chongqing 400047,P.R.China Wei YUAN Academy of Mathematics and Systema Science,Chinese Academy of Sciences,Beijing 100080,P.R.China |
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Abstract: | Letαbe an action of the semi-direct product G ■_σH of countably discrete groups G and H on von Neumann algebra M.Thenβ_h=α_(e,h) AdU_h is an action of H on the von Neumann algebra crossed product M■_αG.We show that M■_α(G■_σH) is ~*-isomorphic to (M ■_αG)■_βH,therefore the crossed product of von Neumann algebras has the associative law. |
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Keywords: | semi-direct product countably discrete groups crossed product von Neumann algebras |
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