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Representations of von Neumann Algebras and Ultraproducts

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dc.contributor.author Haliullin S.
dc.date.accessioned 2021-02-24T20:32:31Z
dc.date.available 2021-02-24T20:32:31Z
dc.date.issued 2020
dc.identifier.issn 0020-7748
dc.identifier.uri https://dspace.kpfu.ru/xmlui/handle/net/160792
dc.description.abstract © 2020, Springer Science+Business Media, LLC, part of Springer Nature. We will introduce the concept of ergodicity of states with respect to some group of transformations on a von Neumann algebra and its properties are studied. A connection between the ergodic states on the von Neumann algebra and the representations of von Neumann algebras associated to them will be described. We also study the properties of ultraproducts of von Neumann algebras with ergodic states and corresponding representations. Here we use ultraproducts of von Neumann algebras by Groh (J. Operator Theory 11(2), 395–404 1984) and Raynaud (J. Operator Theory 48(1), 41–68 2002). In particular, we will show that the ultraproduct of irreducibles representations isn’t, generally speaking, irreducible.
dc.relation.ispartofseries International Journal of Theoretical Physics
dc.subject Ergodic states
dc.subject Representations
dc.subject Ultraproducts
dc.title Representations of von Neumann Algebras and Ultraproducts
dc.type Review
dc.relation.ispartofseries-issue 4
dc.relation.ispartofseries-volume 59
dc.collection Публикации сотрудников КФУ
dc.relation.startpage 1010
dc.source.id SCOPUS00207748-2020-59-4-SID85081027084

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  • Публикации сотрудников КФУ Scopus [24551]
    Коллекция содержит публикации сотрудников Казанского федерального (до 2010 года Казанского государственного) университета, проиндексированные в БД Scopus, начиная с 1970г.

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