Introduction to sofic and hyperlinear groups and Connes' embedding conjecture:
Gespeichert in:
| Beteiligte Personen: | , |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | Englisch |
| Veröffentlicht: |
Cham
Springer
[2015]
|
| Schriftenreihe: | Lecture notes in mathematics
2136 |
| Schlagwörter: | |
| Links: | https://doi.org/10.1007/978-3-319-19333-5 http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=028632577&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=028632577&sequence=000003&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA |
| Umfang: | 1 Online Ressource (VIII, 151 Seiten) |
| ISBN: | 9783319193335 9783319193328 |
| ISSN: | 0075-8434 |
| DOI: | 10.1007/978-3-319-19333-5 |
Internformat
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| adam_text | INTRODUCTION TO SOFIC AND HYPERLINEAR GROUPS AND CONNES EMBEDDING
CONJECTURE
/ CAPRARO, VALERIO
: 2015
TABLE OF CONTENTS / INHALTSVERZEICHNIS
INTRODUCTION
SOFIC AND HYPERLINEAR GROUPS
CONNES EMBEDDING CONJECTURE
CONCLUSIONS
DIESES SCHRIFTSTUECK WURDE MASCHINELL ERZEUGT.
INTRODUCTION TO SOFIC AND HYPERLINEAR GROUPS AND CONNES EMBEDDING
CONJECTURE
/ CAPRARO, VALERIO
: 2015
ABSTRACT / INHALTSTEXT
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
DIESES SCHRIFTSTUECK WURDE MASCHINELL ERZEUGT.
|
| any_adam_object | 1 |
| author | Capraro, Valerio Lupini, Martino |
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| author_facet | Capraro, Valerio Lupini, Martino |
| author_role | aut aut |
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| author_variant | v c vc m l ml |
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| dewey-ones | 512 - Algebra |
| dewey-raw | 512.2 |
| dewey-search | 512.2 |
| dewey-sort | 3512.2 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1007/978-3-319-19333-5 |
| format | Electronic eBook |
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| indexdate | 2024-12-20T17:31:12Z |
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| isbn | 9783319193335 9783319193328 |
| issn | 0075-8434 |
| language | English |
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| series | Lecture notes in mathematics |
| series2 | Lecture notes in mathematics |
| spellingShingle | Capraro, Valerio Lupini, Martino Introduction to sofic and hyperlinear groups and Connes' embedding conjecture Lecture notes in mathematics Mathematics Group theory Operator theory Group Theory and Generalizations Operator Theory Mathematik Universelle Algebra (DE-588)4061777-4 gnd Geometrische Gruppentheorie (DE-588)4651615-3 gnd |
| subject_GND | (DE-588)4061777-4 (DE-588)4651615-3 |
| title | Introduction to sofic and hyperlinear groups and Connes' embedding conjecture |
| title_auth | Introduction to sofic and hyperlinear groups and Connes' embedding conjecture |
| title_exact_search | Introduction to sofic and hyperlinear groups and Connes' embedding conjecture |
| title_full | Introduction to sofic and hyperlinear groups and Connes' embedding conjecture Valerio Capraro, Martino Lupini |
| title_fullStr | Introduction to sofic and hyperlinear groups and Connes' embedding conjecture Valerio Capraro, Martino Lupini |
| title_full_unstemmed | Introduction to sofic and hyperlinear groups and Connes' embedding conjecture Valerio Capraro, Martino Lupini |
| title_short | Introduction to sofic and hyperlinear groups and Connes' embedding conjecture |
| title_sort | introduction to sofic and hyperlinear groups and connes embedding conjecture |
| topic | Mathematics Group theory Operator theory Group Theory and Generalizations Operator Theory Mathematik Universelle Algebra (DE-588)4061777-4 gnd Geometrische Gruppentheorie (DE-588)4651615-3 gnd |
| topic_facet | Mathematics Group theory Operator theory Group Theory and Generalizations Operator Theory Mathematik Universelle Algebra Geometrische Gruppentheorie |
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