On Polish groups of finite type (Q435226)
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scientific article; zbMATH DE number 6054395
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On Polish groups of finite type |
scientific article; zbMATH DE number 6054395 |
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On Polish groups of finite type (English)
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11 July 2012
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Summary: Sorin Popa initiated the study of Polish groups which are embeddable into the unitary group of a separable finite von Neumann algebra. Such groups are called of finite type or said to belong to the class \(\mathcal{U}_{\text{fin}}\). We give necessary and sufficient conditions for Polish groups to be of finite type, and construct examples of such groups from I\(_{\infty}\) and II\(_{\infty}\) von Neumann algebras. We also discuss permanence properties of finite type groups under various algebraic operations. Finally we close the paper with some questions concerning Polish groups of finite type.
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bi-invariant metric
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class \(\mathcal{U}_{\text{fin}}\)
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finite type group
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Polish group
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positive definite function
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SIN-group
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II\(_1\) factor
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