On Polish Groups of Finite Type

Details On Polish Groups of Finite Type On Polish Groups of Finite Type

2011-05-23

arxiv.org/abs/1105.4523v4

Mathematics

Operator Algebras

20 pages

Scientific paper

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. We give necessary and sufficient conditions for Polish groups to be of finite type, and construct exmaples of such groups from semifinite 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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