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Introduction to Sofic and Hyperlinear Groups and Connes' Embedding Conjecture: 2136 (Lecture Notes in Mathematics) - Tapa blanda
Sinopsis
This monograph presents some cornerstone results in the study of sofic and hyperlinear groups and the closely related Connes' embedding conjecture. These notions, as well as the proofs of many results, are presented in the framework of model theory for metric structures. This point of view, rarely explicitly adopted in the literature, clarifies the ideas therein, and provides additional tools to attack open problems.
Sofic and hyperlinear groups are countable discrete groups that can be suitably approximated by finite symmetric groups and groups of unitary matrices. These deep and fruitful notions, introduced by Gromov and Radulescu, respectively, in the late 1990s, stimulated an impressive amount of research in the last 15 years, touching several seemingly distant areas of mathematics including geometric group theory, operator algebras, dynamical systems, graph theory, and quantum information theory. Several long-standing conjectures, still open for arbitrary groups, are now settled for sofic or hyperlinear groups.
The presentation is self-contained and accessible to anyone with a graduate-level mathematical background. In particular, no specific knowledge of logic or model theory is required. The monograph also contains many exercises, to help familiarize the reader with the topics present.
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This monograph presents some cornerstone results in the study of sofic and hyperlinear groups and the closely related Connes' embedding conjecture. These notions, as well as the proofs of many results, are presented in the framework of model theory for metric structures. This point of view, rarely explicitly adopted in the literature, clarifies the ideas therein, and provides additional tools to attack open problems.
Sofic and hyperlinear groups are countable discrete groups that can be suitably approximated by finite symmetric groups and groups of unitary matrices. These deep and fruitful notions, introduced by Gromov and Radulescu, respectively, in the late 1990s, stimulated an impressive amount of research in the last 15 years, touching several seemingly distant areas of mathematics including geometric group theory, operator algebras, dynamical systems, graph theory, and quantum information theory. Several long-standing conjectures, still open for arbitrary groups, are now settled for sofic or hyperlinear groups.
The presentation is self-contained and accessible to anyone with a graduate-level mathematical background. In particular, no specific knowledge of logic or model theory is required. The monograph also contains many exercises, to help familiarize the reader with the topics present.
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Introduction to Sofic and Hyperlinear Groups and Connes' Embedding Conjecture (Lecture Notes in Mathematics)
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Introduction to Sofic and Hyperlinear Groups and Connes' Embedding Conjecture.
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ISBN 10: 3319193325
ISBN 13: 9783319193328
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Introduction to Sofic and Hyperlinear Groups and Connes' Embedding Conjecture (Lecture Notes in Mathematics, 2136)
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Introduction to Sofic and Hyperlinear Groups and Connes' Embedding Conjecture
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Springer International Publishing Okt 2015, 2015
ISBN 10: 3319193325
ISBN 13: 9783319193328
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Taschenbuch. Condición: Neu. This item is printed on demand - it takes 3-4 days longer - Neuware -This monograph presents some cornerstone results in the study of sofic and hyperlinear groups and the closely related Connes' embedding conjecture. These notions, as well as the proofs of many results, are presented in the framework of model theory for metric structures. This point of view, rarely explicitly adopted in the literature, clarifies the ideas therein, and provides additional tools to attack open problems.Sofic and hyperlinear groups are countable discrete groups that can be suitably approximated by finite symmetric groups and groups of unitary matrices. These deep and fruitful notions, introduced by Gromov and Radulescu, respectively, in the late 1990s, stimulated an impressive amount of research in the last 15 years, touching several seemingly distant areas of mathematics including geometric group theory, operator algebras, dynamical systems, graph theory, and quantum information theory. Several long-standing conjectures, still open for arbitrary groups, are now settled for sofic or hyperlinear groups.The presentation is self-contained and accessible to anyone with a graduate-level mathematical background. In particular, no specific knowledge of logic or model theory is required. The monograph also contains many exercises, to help familiarize the reader with the topics present. 164 pp. Englisch. Nº de ref. del artículo: 9783319193328
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Introduction to Sofic and Hyperlinear Groups and Connes' Embedding Conjecture
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Springer International Publishing, 2015
ISBN 10: 3319193325
ISBN 13: 9783319193328
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Taschenbuch. Condición: Neu. Druck auf Anfrage Neuware - Printed after ordering - This monograph presents some cornerstone results in the study of sofic and hyperlinear groups and the closely related Connes' embedding conjecture. These notions, as well as the proofs of many results, are presented in the framework of model theory for metric structures. This point of view, rarely explicitly adopted in the literature, clarifies the ideas therein, and provides additional tools to attack open problems.Sofic and hyperlinear groups are countable discrete groups that can be suitably approximated by finite symmetric groups and groups of unitary matrices. These deep and fruitful notions, introduced by Gromov and Radulescu, respectively, in the late 1990s, stimulated an impressive amount of research in the last 15 years, touching several seemingly distant areas of mathematics including geometric group theory, operator algebras, dynamical systems, graph theory, and quantum information theory. Several long-standing conjectures, still open for arbitrary groups, are now settled for sofic or hyperlinear groups.The presentation is self-contained and accessible to anyone with a graduate-level mathematical background. In particular, no specific knowledge of logic or model theory is required. The monograph also contains many exercises, to help familiarize the reader with the topics present. Nº de ref. del artículo: 9783319193328
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Introduction to Sofic and Hyperlinear Groups and Connes Embedding Conjecture
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Springer International Publishing, 2015
ISBN 10: 3319193325
ISBN 13: 9783319193328
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Condición: New. Dieser Artikel ist ein Print on Demand Artikel und wird nach Ihrer Bestellung fuer Sie gedruckt. Accessible to anyone with a graduate-level mathematical backgroundIncludes many exercises to help the reader to learn quicklyPresents some outstanding open problems in group theory and operator algebrasThis monograph presents som. Nº de ref. del artículo: 34255139
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Introduction to Sofic and Hyperlinear Groups and Connes' Embedding Conjecture (Lecture Notes in Mathematics)
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Introduction to Sofic and Hyperlinear Groups and Connes' Embedding Conjecture (Lecture Notes in Mathematics, 2136)
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Introduction to Sofic and Hyperlinear Groups and Connes' Embedding Conjecture
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Introduction to Sofic and Hyperlinear Groups and Connes' Embedding Conjecture
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Springer International Publishing, Springer International Publishing Okt 2015, 2015
ISBN 10: 3319193325
ISBN 13: 9783319193328
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Taschenbuch. Condición: Neu. This item is printed on demand - Print on Demand Titel. Neuware -This monograph presents some cornerstone results in the study of sofic and hyperlinear groups and the closely related Connes' embedding conjecture. These notions, as well as the proofs of many results, are presented in the framework of model theory for metric structures. This point of view, rarely explicitly adopted in the literature, clarifies the ideas therein, and provides additional tools to attack open problems.Sofic and hyperlinear groups are countable discrete groups that can be suitably approximated by finite symmetric groups and groups of unitary matrices. These deep and fruitful notions, introduced by Gromov and Radulescu, respectively, in the late 1990s, stimulated an impressive amount of research in the last 15 years, touching several seemingly distant areas of mathematics including geometric group theory, operator algebras, dynamical systems, graph theory, and quantum information theory. Several long-standing conjectures, still open for arbitrary groups, are now settled for sofic or hyperlinear groups.The presentation is self-contained and accessible to anyone with a graduate-level mathematical background. In particular, no specific knowledge of logic or model theory is required. The monograph also contains many exercises, to help familiarize the reader with the topics present.Springer Verlag GmbH, Tiergartenstr. 17, 69121 Heidelberg 164 pp. Englisch. Nº de ref. del artículo: 9783319193328
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