Group von Neumann algebras and related algebras:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Abschlussarbeit Buch |
| Sprache: | German |
| Veröffentlicht: |
Göttingen
Math. Inst.
1999
|
| Ausgabe: | Sonderdr. |
| Schriftenreihe: | Mathematica Gottingensis
1999,7 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | II, 161 S. graph. Darst. |
Internformat
MARC
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| 490 | 1 | |a Mathematica Gottingensis |v 1999,7 | |
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Datensatz im Suchindex
| _version_ | 1807504968368783360 |
|---|---|
| adam_text |
CONTENTS
1
INTRODUCTION
1
I
.
I
NOTATIONS
AND
CONVENTIONS
.
5
2
THE
ALGEBRA
OF
OPERATORS
AFFILIATED
TO
A
FINITE
VON
NEUMANN
ALGEBRA
6
3
DIMENSIONS
12
3.1
A-MODULES,//-MODULES
AND
HILBERT
4-MODULCS
.
12
3.2
A
NOTION
OF
DIMENSION
FOR
//-MODULES
.
18
3.3
THE
PASSAGE
FROM
.4-MODULES
TO
//-MODULES
.
23
4
NEW
INTERPRETATION
OF
/^-INVARIANTS
29
5
THE
ATIYAH
CONJECTURE
31
5.1
THE
ATIYAH
CONJECTURE
.
31
5.2
A
STRATEGY
FOR
THE
PROOF
.
35
5.3
THE
RELATION
TO
THE
ISOMORPHISM
CONJECTURE
IN
ALGEBRAIC
I
THEORY
.
39
6
ATIYAH
'
S
CONJECTURE
FOR
THE
FREE
GROUP
ON
TWO
GENERATORS
45
6.1
FREDHOLM
MOD
DES
.
45
6.2
SOME
GEOMETRIC
PROPERTIES
OF
THE
FREE
GROUP
.
18
6.3
CONSTRUCTION
OF
A
FREDHOLM
MODULE
.
19
7
CLASSES
OF
GROUPS
AND
INDUCTION
PRINCIPLES
52
7.1
ELEMENTARY
AMENABLE
GROUPS
.
52
7.2
LINNELL'S
CLASS
C
.
55
8
LINNELL
'
S
THEOREM
62
8.1
INDUCTION
STEP:
EXTENSIONS
-
THE
(A)-PART.
.
66
8.2
INDUCTION
STEP:
EXTENSIONS
-
THE
(B)-PART
.
83
8.3
INDUCTION
STEP:
DIRECTED
UNIONS
.
86
8.1
STARTING
THE
INDUCTION
-
FREE
GROUPS
.
90
8.5
STARTING
THE
INDUCTION
-
FINITE
EXTENSIONS
OF
FREE
GROUPS
.
92
9
HOMOLOGICAL
PROPERTIES
AND
APPLICATIONS
94
10
K-THEORY
98
10
1
A'O
AND
AJ
OF
A
AND
U
.
98
10.2
LOCALIZATION
SEQUENCES
.
103
11
APPENDIX
I:
AFFILIATED
OPERATORS
106
12
APPENDIX
II:
VON
NEUMANN
REGULAR
RINGS
116
13
APPENDIX
III:
LOCALIZATION
OF
NON-COMMUTATIVE
RINGS
119
13.1
ORE
LOCALIZATION
.
119
13.2
UNIVERSAL
LOCALIZATION
.
122
13.3
DIVISION
CLOSURE
AND
RATIONAL
CLOSURE
.
121
13.4
UNIVERSAL
R-FIELDS
.
127
13.5
RECOGNIZING
UNIVERSAL
FIELDS
OF
FRACTIONS
.
130
13.6
LOCALIZATION
WITH
RESPECT
TO
PROJECTIVE
RANK
FUNCTIONS
.
131
14
APPENDIX
IV:
FURTHER
CONCEPTS
FROM
THE
THEORY
OF
RINGS
135
14.1
CROSSED
PRODUCTS
.
135
14.2
MISCELLANEOUS
.
.
138
II |
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| author | Reich, Holger 1969- |
| author_GND | (DE-588)122190858 |
| author_facet | Reich, Holger 1969- |
| author_role | aut |
| author_sort | Reich, Holger 1969- |
| author_variant | h r hr |
| building | Verbundindex |
| bvnumber | BV012692498 |
| classification_tum | MAT 467d |
| ctrlnum | (OCoLC)75998467 (DE-599)BVBBV012692498 |
| discipline | Mathematik |
| edition | Sonderdr. |
| format | Thesis Book |
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| genre | (DE-588)4113937-9 Hochschulschrift gnd-content |
| genre_facet | Hochschulschrift |
| id | DE-604.BV012692498 |
| illustrated | Illustrated |
| indexdate | 2024-08-16T01:17:42Z |
| institution | BVB |
| language | German |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-008627430 |
| oclc_num | 75998467 |
| open_access_boolean | |
| owner | DE-12 DE-91 DE-BY-TUM DE-355 DE-BY-UBR DE-634 DE-11 DE-188 |
| owner_facet | DE-12 DE-91 DE-BY-TUM DE-355 DE-BY-UBR DE-634 DE-11 DE-188 |
| physical | II, 161 S. graph. Darst. |
| publishDate | 1999 |
| publishDateSearch | 1999 |
| publishDateSort | 1999 |
| publisher | Math. Inst. |
| record_format | marc |
| series | Mathematica Gottingensis |
| series2 | Mathematica Gottingensis |
| spelling | Reich, Holger 1969- Verfasser (DE-588)122190858 aut Group von Neumann algebras and related algebras Holger Reich Sonderdr. Göttingen Math. Inst. 1999 II, 161 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Mathematica Gottingensis 1999,7 Zugl.: Göttingen, Univ., Diss., 1999 VonNeumann-Algebra (DE-588)4388395-3 gnd rswk-swf Beschränkter Operator (DE-588)4233452-4 gnd rswk-swf Dimension (DE-588)4149932-3 gnd rswk-swf Gruppe Mathematik (DE-588)4022379-6 gnd rswk-swf (DE-588)4113937-9 Hochschulschrift gnd-content VonNeumann-Algebra (DE-588)4388395-3 s Gruppe Mathematik (DE-588)4022379-6 s Beschränkter Operator (DE-588)4233452-4 s Dimension (DE-588)4149932-3 s DE-604 Mathematica Gottingensis 1999,7 (DE-604)BV000903399 1999,7 DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008627430&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Reich, Holger 1969- Group von Neumann algebras and related algebras Mathematica Gottingensis VonNeumann-Algebra (DE-588)4388395-3 gnd Beschränkter Operator (DE-588)4233452-4 gnd Dimension (DE-588)4149932-3 gnd Gruppe Mathematik (DE-588)4022379-6 gnd |
| subject_GND | (DE-588)4388395-3 (DE-588)4233452-4 (DE-588)4149932-3 (DE-588)4022379-6 (DE-588)4113937-9 |
| title | Group von Neumann algebras and related algebras |
| title_auth | Group von Neumann algebras and related algebras |
| title_exact_search | Group von Neumann algebras and related algebras |
| title_full | Group von Neumann algebras and related algebras Holger Reich |
| title_fullStr | Group von Neumann algebras and related algebras Holger Reich |
| title_full_unstemmed | Group von Neumann algebras and related algebras Holger Reich |
| title_short | Group von Neumann algebras and related algebras |
| title_sort | group von neumann algebras and related algebras |
| topic | VonNeumann-Algebra (DE-588)4388395-3 gnd Beschränkter Operator (DE-588)4233452-4 gnd Dimension (DE-588)4149932-3 gnd Gruppe Mathematik (DE-588)4022379-6 gnd |
| topic_facet | VonNeumann-Algebra Beschränkter Operator Dimension Gruppe Mathematik Hochschulschrift |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008627430&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000903399 |
| work_keys_str_mv | AT reichholger groupvonneumannalgebrasandrelatedalgebras |