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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Abstract

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.

Cite this article

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