JournalsprimsVol. 48, No. 2pp. 389–408

On Polish Groups of Finite Type

  • Hiroshi Ando

    Kyoto University, Japan
  • Yasumichi Matsuzawa

    Hokkaido University, Sapporo, Japan
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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 Ufin\mathscr{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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Hiroshi Ando, Yasumichi Matsuzawa, On Polish Groups of Finite Type. Publ. Res. Inst. Math. Sci. 48 (2012), no. 2, pp. 389–408

DOI 10.2977/PRIMS/73