A note on the classification of gamma factors

One of the earliest invariants introduced in the study of finite von Neumann algebras is the property Gamma of Murray and von Neumann. The set of separable II1 factors can be split in two disjoint subsets: those that have the property Gamma and those that do not have it, called full factors by Conne...

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Autor principal: Sasyk, R.
Formato: JOUR
Materias:
Descriptive set theory
Gamma factors
von Neumann algebras
Acceso en línea:http://hdl.handle.net/20.500.12110/paper_00416932_v57_n1_p1_Sasyk
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Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
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spelling todo:paper_00416932_v57_n1_p1_Sasyk2023-10-03T14:51:22Z A note on the classification of gamma factors Sasyk, R. Descriptive set theory Gamma factors von Neumann algebras One of the earliest invariants introduced in the study of finite von Neumann algebras is the property Gamma of Murray and von Neumann. The set of separable II1 factors can be split in two disjoint subsets: those that have the property Gamma and those that do not have it, called full factors by Connes. In this note we prove that it is not possible to classify separable II1 factors satisfying the property Gamma up to isomorphism by a Borel measurable assignment of countable structures as invariants. We also show that the same holds true for the full II1 factors. Fil:Sasyk, R. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_00416932_v57_n1_p1_Sasyk
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-134
collection Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
topic Descriptive set theory
Gamma factors
von Neumann algebras
spellingShingle Descriptive set theory
Gamma factors
von Neumann algebras
Sasyk, R.
A note on the classification of gamma factors
topic_facet Descriptive set theory
Gamma factors
von Neumann algebras
description One of the earliest invariants introduced in the study of finite von Neumann algebras is the property Gamma of Murray and von Neumann. The set of separable II1 factors can be split in two disjoint subsets: those that have the property Gamma and those that do not have it, called full factors by Connes. In this note we prove that it is not possible to classify separable II1 factors satisfying the property Gamma up to isomorphism by a Borel measurable assignment of countable structures as invariants. We also show that the same holds true for the full II1 factors.
format JOUR
author Sasyk, R.
author_facet Sasyk, R.
author_sort Sasyk, R.
title A note on the classification of gamma factors
title_short A note on the classification of gamma factors
title_full A note on the classification of gamma factors
title_fullStr A note on the classification of gamma factors
title_full_unstemmed A note on the classification of gamma factors
title_sort note on the classification of gamma factors
url http://hdl.handle.net/20.500.12110/paper_00416932_v57_n1_p1_Sasyk
work_keys_str_mv AT sasykr anoteontheclassificationofgammafactors
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