Simple nuclear C∗-algebras not isomorphic to their opposites

Ilijas Farah; Ilan Hirshberg

doi:10.1073/pnas.1619936114

Simple nuclear C∗-algebras not isomorphic to their opposites

Ilijas Farah, Ilan Hirshberg

Department of Mathematics

Ben-Gurion University of the Negev

Research output: Contribution to journal › Article › peer-review

Abstract

We show that it is consistent with Zermelo-Fraenkel set theory with the axiom of choice (ZFC) that there is a simple nuclear nonseparable C-algebra, which is not isomorphic to its opposite algebra. We can furthermore guarantee that this example is an inductive limit of unital copies of the Cuntz algebra O2 or of the canonical anticommutation relations (CAR) algebra.

Original language	American English
Pages (from-to)	6244-6249
Number of pages	6
Journal	Proceedings of the National Academy of Sciences of the United States of America
Volume	114
Issue number	24
DOIs	https://doi.org/10.1073/pnas.1619936114
State	Published - 13 Jun 2017

Keywords

CC∗-algebras
Glimm dichotomy
Jensen's diamond
Naimark's problem
Opposite algebra

All Science Journal Classification (ASJC) codes

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10.1073/pnas.1619936114

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title = "Simple nuclear C∗-algebras not isomorphic to their opposites",

abstract = "We show that it is consistent with Zermelo-Fraenkel set theory with the axiom of choice (ZFC) that there is a simple nuclear nonseparable C-algebra, which is not isomorphic to its opposite algebra. We can furthermore guarantee that this example is an inductive limit of unital copies of the Cuntz algebra O2 or of the canonical anticommutation relations (CAR) algebra.",

keywords = "CC∗-algebras, Glimm dichotomy, Jensen's diamond, Naimark's problem, Opposite algebra",

author = "Ilijas Farah and Ilan Hirshberg",

note = "Funding Information: This research was supported by Israel Science Foundation Grant 476/16 (to I.H.) and Natural Sciences and Engineering Research Council of Canada (I.F.). Most of the work on this paper was done when I.H. was visiting I.F. at the Fields Institute in September 2016. Dedicated to Menachem Magidor on the occasion of his 70th birthday.",

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N2 - We show that it is consistent with Zermelo-Fraenkel set theory with the axiom of choice (ZFC) that there is a simple nuclear nonseparable C-algebra, which is not isomorphic to its opposite algebra. We can furthermore guarantee that this example is an inductive limit of unital copies of the Cuntz algebra O2 or of the canonical anticommutation relations (CAR) algebra.

AB - We show that it is consistent with Zermelo-Fraenkel set theory with the axiom of choice (ZFC) that there is a simple nuclear nonseparable C-algebra, which is not isomorphic to its opposite algebra. We can furthermore guarantee that this example is an inductive limit of unital copies of the Cuntz algebra O2 or of the canonical anticommutation relations (CAR) algebra.

KW - CC∗-algebras

KW - Glimm dichotomy

KW - Jensen's diamond

KW - Naimark's problem

KW - Opposite algebra

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JF - Proceedings of the National Academy of Sciences of the United States of America

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ER -

Simple nuclear C∗-algebras not isomorphic to their opposites

Abstract

Keywords

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