Classification of actions of discrete Kac algebras on injective factors:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Providence, Rhode Island
American Mathematical Society
January 2017
|
| Schriftenreihe: | Memoirs of the American Mathematical Society
1160 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | ix, 118 Seiten |
| ISBN: | 9781470420550 |
Internformat
MARC
| LEADER | 00000nam a2200000 cb4500 | ||
|---|---|---|---|
| 001 | BV044047569 | ||
| 003 | DE-604 | ||
| 005 | 20210922 | ||
| 007 | t | ||
| 008 | 170217s2017 |||| 00||| eng d | ||
| 020 | |a 9781470420550 |9 978-1-4704-2055-0 | ||
| 035 | |a (OCoLC)971480451 | ||
| 035 | |a (DE-599)BVBBV044047569 | ||
| 040 | |a DE-604 |b ger |e rda | ||
| 041 | 0 | |a eng | |
| 049 | |a DE-355 |a DE-83 |a DE-29T |a DE-11 | ||
| 082 | 0 | |a 512.482 | |
| 084 | |a 46L55 |2 msc | ||
| 084 | |a 46L65 |2 msc | ||
| 100 | 1 | |a Masuda, Toshihiko |0 (DE-588)1117227367 |4 aut | |
| 245 | 1 | 0 | |a Classification of actions of discrete Kac algebras on injective factors |c Toshihiko Masuda, Reiji Tomatsu |
| 264 | 1 | |a Providence, Rhode Island |b American Mathematical Society |c January 2017 | |
| 300 | |a ix, 118 Seiten | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Memoirs of the American Mathematical Society |v volume 245, number 1160 (5th of 6 numbers) | |
| 650 | 0 | 7 | |a Injektiver Modul |0 (DE-588)4161753-8 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Kac-Moody-Algebra |0 (DE-588)4223399-9 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Lie-Algebra |0 (DE-588)4130355-6 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Kac-Moody-Algebra |0 (DE-588)4223399-9 |D s |
| 689 | 0 | 1 | |a Lie-Algebra |0 (DE-588)4130355-6 |D s |
| 689 | 0 | 2 | |a Injektiver Modul |0 (DE-588)4161753-8 |D s |
| 689 | 0 | |5 DE-604 | |
| 700 | 1 | |a Tomatsu, Reiji |d 1978- |0 (DE-588)1117227405 |4 aut | |
| 776 | 0 | 8 | |i Erscheint auch als |n Online-Ausgabe |z 978-1-4704-3609-4 |
| 830 | 0 | |a Memoirs of the American Mathematical Society |v 1160 |w (DE-604)BV008000141 |9 1160 | |
| 856 | 4 | 2 | |m Digitalisierung UB Regensburg - ADAM Catalogue Enrichment |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=029454477&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-029454477 | ||
Datensatz im Suchindex
| _version_ | 1804177062794100737 |
|---|---|
| adam_text | Contents
Introduction vii
Chapter 1* Preliminary 1
1.1. Notation and terminology 1
1.2. Canonical extensions 1
1.3. Modular endomorphisms 3
1.4. Ultraproduct von Neumann algebras 3
Chapter 2. Canonical extension of irreducible endomorphisms 7
2.1. Decomposition of the canonical extension of an endomorphism 7
2.2. Extended modular automorphisms 13
Chapter 3. Kac algebras 15
3.1. Compact or discrete Kac algebras 15
3.2. Generalized central quantum subgroups 16
3.3. Normal subcategory 17
3.4. 2-cocycles of a discrete Kac algebra 18
3.5. Skew symmetric bicharacters 20
3.6. A Kac algebra associated with ¡3^ 23
3.7. Actions and Cocycle actions 24
3.8. Dual actions of finite groups 27
3.9. Actions of Sd 28
Chapter 4. Classification of modular kernels 31
4.1. Modular kernels 31
4.2. Models of modular kernels 40
Chapter 5. Classification of actions with non-trivial modular parts 45
5.1. Discrete group F 45
5.2. Invariants of actions 48
5.3. Model action 1 51
5.4. Model action 2 53
5.5. Modular actions 55
5.6. Examples 57
5.7. Crossed products 58
5.8. Hamachi-Kosaki decomposition 60
Chapter 6. Classification of centrally free actions 63
6.1. Settings 63
6.2. Action 7 64
6.3. Rohlin tower 66
iii
IV
CONTENTS
6.4. Almost vanishing theorem of approximate 1-cocycles 78
6.5. 2-cohomology vanishing 85
6.6. Intertwining cocycles 86
6.7. Intertwining argument 94
Chapter 7. Related problems 99
7.1. 1-cohomology of an ergodic flow 99
7.2. Invariants for general actions 99
Chapter 8. Appendix 101
8.1. Index theory for von Neumann algebras 101
8.2. Index of an endomorphism 105
8.3. Cocycle crossed product 108
8.4. Dual cocycle twisting of a Kac algebra 109
Bibliography 113
Index 117
|
| any_adam_object | 1 |
| author | Masuda, Toshihiko Tomatsu, Reiji 1978- |
| author_GND | (DE-588)1117227367 (DE-588)1117227405 |
| author_facet | Masuda, Toshihiko Tomatsu, Reiji 1978- |
| author_role | aut aut |
| author_sort | Masuda, Toshihiko |
| author_variant | t m tm r t rt |
| building | Verbundindex |
| bvnumber | BV044047569 |
| ctrlnum | (OCoLC)971480451 (DE-599)BVBBV044047569 |
| dewey-full | 512.482 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
| dewey-raw | 512.482 |
| dewey-search | 512.482 |
| dewey-sort | 3512.482 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01900nam a2200433 cb4500</leader><controlfield tag="001">BV044047569</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">20210922 </controlfield><controlfield tag="007">t</controlfield><controlfield tag="008">170217s2017 |||| 00||| eng d</controlfield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9781470420550</subfield><subfield code="9">978-1-4704-2055-0</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)971480451</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV044047569</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield><subfield code="e">rda</subfield></datafield><datafield tag="041" ind1="0" ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-355</subfield><subfield code="a">DE-83</subfield><subfield code="a">DE-29T</subfield><subfield code="a">DE-11</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">512.482</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">46L55</subfield><subfield code="2">msc</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">46L65</subfield><subfield code="2">msc</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Masuda, Toshihiko</subfield><subfield code="0">(DE-588)1117227367</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Classification of actions of discrete Kac algebras on injective factors</subfield><subfield code="c">Toshihiko Masuda, Reiji Tomatsu</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Providence, Rhode Island</subfield><subfield code="b">American Mathematical Society</subfield><subfield code="c">January 2017</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">ix, 118 Seiten</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="b">n</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="b">nc</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="490" ind1="1" ind2=" "><subfield code="a">Memoirs of the American Mathematical Society</subfield><subfield code="v">volume 245, number 1160 (5th of 6 numbers)</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Injektiver Modul</subfield><subfield code="0">(DE-588)4161753-8</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Kac-Moody-Algebra</subfield><subfield code="0">(DE-588)4223399-9</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Lie-Algebra</subfield><subfield code="0">(DE-588)4130355-6</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="689" ind1="0" ind2="0"><subfield code="a">Kac-Moody-Algebra</subfield><subfield code="0">(DE-588)4223399-9</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2="1"><subfield code="a">Lie-Algebra</subfield><subfield code="0">(DE-588)4130355-6</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2="2"><subfield code="a">Injektiver Modul</subfield><subfield code="0">(DE-588)4161753-8</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2=" "><subfield code="5">DE-604</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Tomatsu, Reiji</subfield><subfield code="d">1978-</subfield><subfield code="0">(DE-588)1117227405</subfield><subfield code="4">aut</subfield></datafield><datafield tag="776" ind1="0" ind2="8"><subfield code="i">Erscheint auch als</subfield><subfield code="n">Online-Ausgabe</subfield><subfield code="z">978-1-4704-3609-4</subfield></datafield><datafield tag="830" ind1=" " ind2="0"><subfield code="a">Memoirs of the American Mathematical Society</subfield><subfield code="v">1160</subfield><subfield code="w">(DE-604)BV008000141</subfield><subfield code="9">1160</subfield></datafield><datafield tag="856" ind1="4" ind2="2"><subfield code="m">Digitalisierung UB Regensburg - ADAM Catalogue Enrichment</subfield><subfield code="q">application/pdf</subfield><subfield code="u">http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=029454477&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA</subfield><subfield code="3">Inhaltsverzeichnis</subfield></datafield><datafield tag="999" ind1=" " ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-029454477</subfield></datafield></record></collection> |
| id | DE-604.BV044047569 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T07:42:07Z |
| institution | BVB |
| isbn | 9781470420550 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-029454477 |
| oclc_num | 971480451 |
| open_access_boolean | |
| owner | DE-355 DE-BY-UBR DE-83 DE-29T DE-11 |
| owner_facet | DE-355 DE-BY-UBR DE-83 DE-29T DE-11 |
| physical | ix, 118 Seiten |
| publishDate | 2017 |
| publishDateSearch | 2017 |
| publishDateSort | 2017 |
| publisher | American Mathematical Society |
| record_format | marc |
| series | Memoirs of the American Mathematical Society |
| series2 | Memoirs of the American Mathematical Society |
| spelling | Masuda, Toshihiko (DE-588)1117227367 aut Classification of actions of discrete Kac algebras on injective factors Toshihiko Masuda, Reiji Tomatsu Providence, Rhode Island American Mathematical Society January 2017 ix, 118 Seiten txt rdacontent n rdamedia nc rdacarrier Memoirs of the American Mathematical Society volume 245, number 1160 (5th of 6 numbers) Injektiver Modul (DE-588)4161753-8 gnd rswk-swf Kac-Moody-Algebra (DE-588)4223399-9 gnd rswk-swf Lie-Algebra (DE-588)4130355-6 gnd rswk-swf Kac-Moody-Algebra (DE-588)4223399-9 s Lie-Algebra (DE-588)4130355-6 s Injektiver Modul (DE-588)4161753-8 s DE-604 Tomatsu, Reiji 1978- (DE-588)1117227405 aut Erscheint auch als Online-Ausgabe 978-1-4704-3609-4 Memoirs of the American Mathematical Society 1160 (DE-604)BV008000141 1160 Digitalisierung UB Regensburg - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=029454477&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Masuda, Toshihiko Tomatsu, Reiji 1978- Classification of actions of discrete Kac algebras on injective factors Memoirs of the American Mathematical Society Injektiver Modul (DE-588)4161753-8 gnd Kac-Moody-Algebra (DE-588)4223399-9 gnd Lie-Algebra (DE-588)4130355-6 gnd |
| subject_GND | (DE-588)4161753-8 (DE-588)4223399-9 (DE-588)4130355-6 |
| title | Classification of actions of discrete Kac algebras on injective factors |
| title_auth | Classification of actions of discrete Kac algebras on injective factors |
| title_exact_search | Classification of actions of discrete Kac algebras on injective factors |
| title_full | Classification of actions of discrete Kac algebras on injective factors Toshihiko Masuda, Reiji Tomatsu |
| title_fullStr | Classification of actions of discrete Kac algebras on injective factors Toshihiko Masuda, Reiji Tomatsu |
| title_full_unstemmed | Classification of actions of discrete Kac algebras on injective factors Toshihiko Masuda, Reiji Tomatsu |
| title_short | Classification of actions of discrete Kac algebras on injective factors |
| title_sort | classification of actions of discrete kac algebras on injective factors |
| topic | Injektiver Modul (DE-588)4161753-8 gnd Kac-Moody-Algebra (DE-588)4223399-9 gnd Lie-Algebra (DE-588)4130355-6 gnd |
| topic_facet | Injektiver Modul Kac-Moody-Algebra Lie-Algebra |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=029454477&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV008000141 |
| work_keys_str_mv | AT masudatoshihiko classificationofactionsofdiscretekacalgebrasoninjectivefactors AT tomatsureiji classificationofactionsofdiscretekacalgebrasoninjectivefactors |