Structure of bicentralizer algebras and inclusions of type $$\mathrm{III}$$ factors
Abstract We investigate the structure of the relative bicentralizer algebra $$\mathrm{B}(N \subset M, \varphi )$$ for inclusions of von Neumann algebras with normal expectation where N is a type $$\mathrm{III}_1$$ subfactor and $$\varphi \in N_*$$ is a faithful state. We first construct a canonical...
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| Autor*in: |
Ando, Hiroshi [verfasserIn] |
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| Format: |
Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2019 |
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| Anmerkung: |
© Springer-Verlag GmbH Germany, part of Springer Nature 2019 |
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| Übergeordnetes Werk: |
Enthalten in: Mathematische Annalen - Springer Berlin Heidelberg, 1869, 376(2019), 3-4 vom: 30. Nov., Seite 1145-1194 |
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| Übergeordnetes Werk: |
volume:376 ; year:2019 ; number:3-4 ; day:30 ; month:11 ; pages:1145-1194 |
| Links: |
|---|
| DOI / URN: |
10.1007/s00208-019-01939-9 |
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OLC2039634851 |
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| 520 | |a Abstract We investigate the structure of the relative bicentralizer algebra $$\mathrm{B}(N \subset M, \varphi )$$ for inclusions of von Neumann algebras with normal expectation where N is a type $$\mathrm{III}_1$$ subfactor and $$\varphi \in N_*$$ is a faithful state. We first construct a canonical flow $$\beta ^\varphi : \mathbf {R}^*_+ \curvearrowright \mathrm{B}(N \subset M, \varphi )$$ on the relative bicentralizer algebra and we show that the W$$^*$$-dynamical system $$(\mathrm{B}(N \subset M, \varphi ), \beta ^\varphi )$$ is independent of the choice of $$\varphi $$ up to a canonical isomorphism. In the case when $$N=M$$, we deduce new results on the structure of the automorphism group of $$\mathrm{B}(M,\varphi )$$ and we relate the period of the flow $$\beta ^\varphi $$ to the tensorial absorption of Powers factors. For general irreducible inclusions $$N \subset M$$, we relate the ergodicity of the flow $$\beta ^\varphi $$ to the existence of irreducible AFD subfactors in M that sit with normal expectation in N. When the inclusion $$N \subset M$$ is discrete, we prove a relative bicentralizer theorem and we use it to solve Kadison’s problem when N is amenable. | ||
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10.1007/s00208-019-01939-9 doi (DE-627)OLC2039634851 (DE-He213)s00208-019-01939-9-p DE-627 ger DE-627 rakwb eng 510 VZ 510 VZ 17,1 ssgn 31.00 bkl Ando, Hiroshi verfasserin aut Structure of bicentralizer algebras and inclusions of type $$\mathrm{III}$$ factors 2019 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer-Verlag GmbH Germany, part of Springer Nature 2019 Abstract We investigate the structure of the relative bicentralizer algebra $$\mathrm{B}(N \subset M, \varphi )$$ for inclusions of von Neumann algebras with normal expectation where N is a type $$\mathrm{III}_1$$ subfactor and $$\varphi \in N_*$$ is a faithful state. We first construct a canonical flow $$\beta ^\varphi : \mathbf {R}^*_+ \curvearrowright \mathrm{B}(N \subset M, \varphi )$$ on the relative bicentralizer algebra and we show that the W$$^*$$-dynamical system $$(\mathrm{B}(N \subset M, \varphi ), \beta ^\varphi )$$ is independent of the choice of $$\varphi $$ up to a canonical isomorphism. In the case when $$N=M$$, we deduce new results on the structure of the automorphism group of $$\mathrm{B}(M,\varphi )$$ and we relate the period of the flow $$\beta ^\varphi $$ to the tensorial absorption of Powers factors. For general irreducible inclusions $$N \subset M$$, we relate the ergodicity of the flow $$\beta ^\varphi $$ to the existence of irreducible AFD subfactors in M that sit with normal expectation in N. When the inclusion $$N \subset M$$ is discrete, we prove a relative bicentralizer theorem and we use it to solve Kadison’s problem when N is amenable. Haagerup, Uffe aut Houdayer, Cyril (orcid)0000-0002-5953-263X aut Marrakchi, Amine aut Enthalten in Mathematische Annalen Springer Berlin Heidelberg, 1869 376(2019), 3-4 vom: 30. Nov., Seite 1145-1194 (DE-627)129060151 (DE-600)285-9 (DE-576)014390825 0025-5831 nnns volume:376 year:2019 number:3-4 day:30 month:11 pages:1145-1194 https://doi.org/10.1007/s00208-019-01939-9 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT SSG-OPC-FOR GBV_ILN_40 GBV_ILN_70 GBV_ILN_2007 GBV_ILN_2018 GBV_ILN_2030 GBV_ILN_2409 GBV_ILN_4027 GBV_ILN_4126 GBV_ILN_4277 GBV_ILN_4306 31.00 Mathematik: Allgemeines Mathematik: Allgemeines VZ AR 376 2019 3-4 30 11 1145-1194 |
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10.1007/s00208-019-01939-9 doi (DE-627)OLC2039634851 (DE-He213)s00208-019-01939-9-p DE-627 ger DE-627 rakwb eng 510 VZ 510 VZ 17,1 ssgn 31.00 bkl Ando, Hiroshi verfasserin aut Structure of bicentralizer algebras and inclusions of type $$\mathrm{III}$$ factors 2019 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer-Verlag GmbH Germany, part of Springer Nature 2019 Abstract We investigate the structure of the relative bicentralizer algebra $$\mathrm{B}(N \subset M, \varphi )$$ for inclusions of von Neumann algebras with normal expectation where N is a type $$\mathrm{III}_1$$ subfactor and $$\varphi \in N_*$$ is a faithful state. We first construct a canonical flow $$\beta ^\varphi : \mathbf {R}^*_+ \curvearrowright \mathrm{B}(N \subset M, \varphi )$$ on the relative bicentralizer algebra and we show that the W$$^*$$-dynamical system $$(\mathrm{B}(N \subset M, \varphi ), \beta ^\varphi )$$ is independent of the choice of $$\varphi $$ up to a canonical isomorphism. In the case when $$N=M$$, we deduce new results on the structure of the automorphism group of $$\mathrm{B}(M,\varphi )$$ and we relate the period of the flow $$\beta ^\varphi $$ to the tensorial absorption of Powers factors. For general irreducible inclusions $$N \subset M$$, we relate the ergodicity of the flow $$\beta ^\varphi $$ to the existence of irreducible AFD subfactors in M that sit with normal expectation in N. When the inclusion $$N \subset M$$ is discrete, we prove a relative bicentralizer theorem and we use it to solve Kadison’s problem when N is amenable. Haagerup, Uffe aut Houdayer, Cyril (orcid)0000-0002-5953-263X aut Marrakchi, Amine aut Enthalten in Mathematische Annalen Springer Berlin Heidelberg, 1869 376(2019), 3-4 vom: 30. Nov., Seite 1145-1194 (DE-627)129060151 (DE-600)285-9 (DE-576)014390825 0025-5831 nnns volume:376 year:2019 number:3-4 day:30 month:11 pages:1145-1194 https://doi.org/10.1007/s00208-019-01939-9 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT SSG-OPC-FOR GBV_ILN_40 GBV_ILN_70 GBV_ILN_2007 GBV_ILN_2018 GBV_ILN_2030 GBV_ILN_2409 GBV_ILN_4027 GBV_ILN_4126 GBV_ILN_4277 GBV_ILN_4306 31.00 Mathematik: Allgemeines Mathematik: Allgemeines VZ AR 376 2019 3-4 30 11 1145-1194 |
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10.1007/s00208-019-01939-9 doi (DE-627)OLC2039634851 (DE-He213)s00208-019-01939-9-p DE-627 ger DE-627 rakwb eng 510 VZ 510 VZ 17,1 ssgn 31.00 bkl Ando, Hiroshi verfasserin aut Structure of bicentralizer algebras and inclusions of type $$\mathrm{III}$$ factors 2019 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer-Verlag GmbH Germany, part of Springer Nature 2019 Abstract We investigate the structure of the relative bicentralizer algebra $$\mathrm{B}(N \subset M, \varphi )$$ for inclusions of von Neumann algebras with normal expectation where N is a type $$\mathrm{III}_1$$ subfactor and $$\varphi \in N_*$$ is a faithful state. We first construct a canonical flow $$\beta ^\varphi : \mathbf {R}^*_+ \curvearrowright \mathrm{B}(N \subset M, \varphi )$$ on the relative bicentralizer algebra and we show that the W$$^*$$-dynamical system $$(\mathrm{B}(N \subset M, \varphi ), \beta ^\varphi )$$ is independent of the choice of $$\varphi $$ up to a canonical isomorphism. In the case when $$N=M$$, we deduce new results on the structure of the automorphism group of $$\mathrm{B}(M,\varphi )$$ and we relate the period of the flow $$\beta ^\varphi $$ to the tensorial absorption of Powers factors. For general irreducible inclusions $$N \subset M$$, we relate the ergodicity of the flow $$\beta ^\varphi $$ to the existence of irreducible AFD subfactors in M that sit with normal expectation in N. When the inclusion $$N \subset M$$ is discrete, we prove a relative bicentralizer theorem and we use it to solve Kadison’s problem when N is amenable. Haagerup, Uffe aut Houdayer, Cyril (orcid)0000-0002-5953-263X aut Marrakchi, Amine aut Enthalten in Mathematische Annalen Springer Berlin Heidelberg, 1869 376(2019), 3-4 vom: 30. Nov., Seite 1145-1194 (DE-627)129060151 (DE-600)285-9 (DE-576)014390825 0025-5831 nnns volume:376 year:2019 number:3-4 day:30 month:11 pages:1145-1194 https://doi.org/10.1007/s00208-019-01939-9 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT SSG-OPC-FOR GBV_ILN_40 GBV_ILN_70 GBV_ILN_2007 GBV_ILN_2018 GBV_ILN_2030 GBV_ILN_2409 GBV_ILN_4027 GBV_ILN_4126 GBV_ILN_4277 GBV_ILN_4306 31.00 Mathematik: Allgemeines Mathematik: Allgemeines VZ AR 376 2019 3-4 30 11 1145-1194 |
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10.1007/s00208-019-01939-9 doi (DE-627)OLC2039634851 (DE-He213)s00208-019-01939-9-p DE-627 ger DE-627 rakwb eng 510 VZ 510 VZ 17,1 ssgn 31.00 bkl Ando, Hiroshi verfasserin aut Structure of bicentralizer algebras and inclusions of type $$\mathrm{III}$$ factors 2019 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer-Verlag GmbH Germany, part of Springer Nature 2019 Abstract We investigate the structure of the relative bicentralizer algebra $$\mathrm{B}(N \subset M, \varphi )$$ for inclusions of von Neumann algebras with normal expectation where N is a type $$\mathrm{III}_1$$ subfactor and $$\varphi \in N_*$$ is a faithful state. We first construct a canonical flow $$\beta ^\varphi : \mathbf {R}^*_+ \curvearrowright \mathrm{B}(N \subset M, \varphi )$$ on the relative bicentralizer algebra and we show that the W$$^*$$-dynamical system $$(\mathrm{B}(N \subset M, \varphi ), \beta ^\varphi )$$ is independent of the choice of $$\varphi $$ up to a canonical isomorphism. In the case when $$N=M$$, we deduce new results on the structure of the automorphism group of $$\mathrm{B}(M,\varphi )$$ and we relate the period of the flow $$\beta ^\varphi $$ to the tensorial absorption of Powers factors. For general irreducible inclusions $$N \subset M$$, we relate the ergodicity of the flow $$\beta ^\varphi $$ to the existence of irreducible AFD subfactors in M that sit with normal expectation in N. When the inclusion $$N \subset M$$ is discrete, we prove a relative bicentralizer theorem and we use it to solve Kadison’s problem when N is amenable. Haagerup, Uffe aut Houdayer, Cyril (orcid)0000-0002-5953-263X aut Marrakchi, Amine aut Enthalten in Mathematische Annalen Springer Berlin Heidelberg, 1869 376(2019), 3-4 vom: 30. Nov., Seite 1145-1194 (DE-627)129060151 (DE-600)285-9 (DE-576)014390825 0025-5831 nnns volume:376 year:2019 number:3-4 day:30 month:11 pages:1145-1194 https://doi.org/10.1007/s00208-019-01939-9 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT SSG-OPC-FOR GBV_ILN_40 GBV_ILN_70 GBV_ILN_2007 GBV_ILN_2018 GBV_ILN_2030 GBV_ILN_2409 GBV_ILN_4027 GBV_ILN_4126 GBV_ILN_4277 GBV_ILN_4306 31.00 Mathematik: Allgemeines Mathematik: Allgemeines VZ AR 376 2019 3-4 30 11 1145-1194 |
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10.1007/s00208-019-01939-9 doi (DE-627)OLC2039634851 (DE-He213)s00208-019-01939-9-p DE-627 ger DE-627 rakwb eng 510 VZ 510 VZ 17,1 ssgn 31.00 bkl Ando, Hiroshi verfasserin aut Structure of bicentralizer algebras and inclusions of type $$\mathrm{III}$$ factors 2019 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer-Verlag GmbH Germany, part of Springer Nature 2019 Abstract We investigate the structure of the relative bicentralizer algebra $$\mathrm{B}(N \subset M, \varphi )$$ for inclusions of von Neumann algebras with normal expectation where N is a type $$\mathrm{III}_1$$ subfactor and $$\varphi \in N_*$$ is a faithful state. We first construct a canonical flow $$\beta ^\varphi : \mathbf {R}^*_+ \curvearrowright \mathrm{B}(N \subset M, \varphi )$$ on the relative bicentralizer algebra and we show that the W$$^*$$-dynamical system $$(\mathrm{B}(N \subset M, \varphi ), \beta ^\varphi )$$ is independent of the choice of $$\varphi $$ up to a canonical isomorphism. In the case when $$N=M$$, we deduce new results on the structure of the automorphism group of $$\mathrm{B}(M,\varphi )$$ and we relate the period of the flow $$\beta ^\varphi $$ to the tensorial absorption of Powers factors. For general irreducible inclusions $$N \subset M$$, we relate the ergodicity of the flow $$\beta ^\varphi $$ to the existence of irreducible AFD subfactors in M that sit with normal expectation in N. When the inclusion $$N \subset M$$ is discrete, we prove a relative bicentralizer theorem and we use it to solve Kadison’s problem when N is amenable. Haagerup, Uffe aut Houdayer, Cyril (orcid)0000-0002-5953-263X aut Marrakchi, Amine aut Enthalten in Mathematische Annalen Springer Berlin Heidelberg, 1869 376(2019), 3-4 vom: 30. Nov., Seite 1145-1194 (DE-627)129060151 (DE-600)285-9 (DE-576)014390825 0025-5831 nnns volume:376 year:2019 number:3-4 day:30 month:11 pages:1145-1194 https://doi.org/10.1007/s00208-019-01939-9 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT SSG-OPC-FOR GBV_ILN_40 GBV_ILN_70 GBV_ILN_2007 GBV_ILN_2018 GBV_ILN_2030 GBV_ILN_2409 GBV_ILN_4027 GBV_ILN_4126 GBV_ILN_4277 GBV_ILN_4306 31.00 Mathematik: Allgemeines Mathematik: Allgemeines VZ AR 376 2019 3-4 30 11 1145-1194 |
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Enthalten in Mathematische Annalen 376(2019), 3-4 vom: 30. Nov., Seite 1145-1194 volume:376 year:2019 number:3-4 day:30 month:11 pages:1145-1194 |
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Ando, Hiroshi @@aut@@ Haagerup, Uffe @@aut@@ Houdayer, Cyril @@aut@@ Marrakchi, Amine @@aut@@ |
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structure of bicentralizer algebras and inclusions of type $$\mathrm{iii}$$ factors |
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Structure of bicentralizer algebras and inclusions of type $$\mathrm{III}$$ factors |
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Abstract We investigate the structure of the relative bicentralizer algebra $$\mathrm{B}(N \subset M, \varphi )$$ for inclusions of von Neumann algebras with normal expectation where N is a type $$\mathrm{III}_1$$ subfactor and $$\varphi \in N_*$$ is a faithful state. We first construct a canonical flow $$\beta ^\varphi : \mathbf {R}^*_+ \curvearrowright \mathrm{B}(N \subset M, \varphi )$$ on the relative bicentralizer algebra and we show that the W$$^*$$-dynamical system $$(\mathrm{B}(N \subset M, \varphi ), \beta ^\varphi )$$ is independent of the choice of $$\varphi $$ up to a canonical isomorphism. In the case when $$N=M$$, we deduce new results on the structure of the automorphism group of $$\mathrm{B}(M,\varphi )$$ and we relate the period of the flow $$\beta ^\varphi $$ to the tensorial absorption of Powers factors. For general irreducible inclusions $$N \subset M$$, we relate the ergodicity of the flow $$\beta ^\varphi $$ to the existence of irreducible AFD subfactors in M that sit with normal expectation in N. When the inclusion $$N \subset M$$ is discrete, we prove a relative bicentralizer theorem and we use it to solve Kadison’s problem when N is amenable. © Springer-Verlag GmbH Germany, part of Springer Nature 2019 |
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Abstract We investigate the structure of the relative bicentralizer algebra $$\mathrm{B}(N \subset M, \varphi )$$ for inclusions of von Neumann algebras with normal expectation where N is a type $$\mathrm{III}_1$$ subfactor and $$\varphi \in N_*$$ is a faithful state. We first construct a canonical flow $$\beta ^\varphi : \mathbf {R}^*_+ \curvearrowright \mathrm{B}(N \subset M, \varphi )$$ on the relative bicentralizer algebra and we show that the W$$^*$$-dynamical system $$(\mathrm{B}(N \subset M, \varphi ), \beta ^\varphi )$$ is independent of the choice of $$\varphi $$ up to a canonical isomorphism. In the case when $$N=M$$, we deduce new results on the structure of the automorphism group of $$\mathrm{B}(M,\varphi )$$ and we relate the period of the flow $$\beta ^\varphi $$ to the tensorial absorption of Powers factors. For general irreducible inclusions $$N \subset M$$, we relate the ergodicity of the flow $$\beta ^\varphi $$ to the existence of irreducible AFD subfactors in M that sit with normal expectation in N. When the inclusion $$N \subset M$$ is discrete, we prove a relative bicentralizer theorem and we use it to solve Kadison’s problem when N is amenable. © Springer-Verlag GmbH Germany, part of Springer Nature 2019 |
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Abstract We investigate the structure of the relative bicentralizer algebra $$\mathrm{B}(N \subset M, \varphi )$$ for inclusions of von Neumann algebras with normal expectation where N is a type $$\mathrm{III}_1$$ subfactor and $$\varphi \in N_*$$ is a faithful state. We first construct a canonical flow $$\beta ^\varphi : \mathbf {R}^*_+ \curvearrowright \mathrm{B}(N \subset M, \varphi )$$ on the relative bicentralizer algebra and we show that the W$$^*$$-dynamical system $$(\mathrm{B}(N \subset M, \varphi ), \beta ^\varphi )$$ is independent of the choice of $$\varphi $$ up to a canonical isomorphism. In the case when $$N=M$$, we deduce new results on the structure of the automorphism group of $$\mathrm{B}(M,\varphi )$$ and we relate the period of the flow $$\beta ^\varphi $$ to the tensorial absorption of Powers factors. For general irreducible inclusions $$N \subset M$$, we relate the ergodicity of the flow $$\beta ^\varphi $$ to the existence of irreducible AFD subfactors in M that sit with normal expectation in N. When the inclusion $$N \subset M$$ is discrete, we prove a relative bicentralizer theorem and we use it to solve Kadison’s problem when N is amenable. © Springer-Verlag GmbH Germany, part of Springer Nature 2019 |
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