Journal article
Groups of measure space transformations and invariants of outer conjugation for automorphisms from normalizers of type III full groups
Journal of Functional Analysis, Vol.60(3), pp.341-369
1985
DOI: 10.1016/0022-1236(85)90044-8
Abstract
The necessary and sufficient conditions of outer conjugation for automorphisms from the normalizer of approximated III type groups are found. Let T be an automorphism of a Lebesgue space ( X , μ ) of the III 0 type, [ T ] the full group generated by T , N [ T ] its normalizer, { W t ( T )} the flow associated with T and α → mod α the homomorphism from N [ T ] to C { W } the centralizer of the associated flow. The following results are obtained: ∀α ∈ C{W} ∃ \ ̂ ga ∈ N[T] such that mod \ ̂ ga = α; automorphisms α 1 , and α 2 from N [ T ] are outer conjugate if and only if p ( α 1 ) = p ( α 2 ), mod α 1 = γ mod α 2 γ −1 , where γ ∈ C { W } and p (·) is the outer period; the canonical form of the elements from N [ T ] is found. The case is also considered where T is types III λ (0 < λ < 1) and III 1 .
Details
- Title: Subtitle
- Groups of measure space transformations and invariants of outer conjugation for automorphisms from normalizers of type III full groups
- Creators
- S. I BezuglyiV. Ya Golodets
- Resource Type
- Journal article
- Publication Details
- Journal of Functional Analysis, Vol.60(3), pp.341-369
- DOI
- 10.1016/0022-1236(85)90044-8
- ISSN
- 1096-0783
- eISSN
- 1096-0783
- Language
- English
- Date published
- 1985
- Academic Unit
- Mathematics
- Record Identifier
- 9983985822902771
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