Linear representations of finite groups:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English French |
| Published: |
New York ; Berlin ; Heidelberg ; London ; Paris ; Tokyo ; Hong K
Springer
1993
|
| Edition: | Corr. 4. pr. |
| Series: | Graduate texts in mathematics
42 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Literaturangaben |
| Physical Description: | X, 170 S. graph. Darst. |
| ISBN: | 3540901906 0387901906 |
Staff View
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| 240 | 1 | 0 | |a Représentations linéaires des groupes finis |
| 245 | 1 | 0 | |a Linear representations of finite groups |c Jean-Pierre Serre. Transl. from the French by Leonard L. Scott |
| 250 | |a Corr. 4. pr. | ||
| 264 | 1 | |a New York ; Berlin ; Heidelberg ; London ; Paris ; Tokyo ; Hong K |b Springer |c 1993 | |
| 300 | |a X, 170 S. |b graph. Darst. | ||
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| 490 | 1 | |a Graduate texts in mathematics |v 42 | |
| 500 | |a Literaturangaben | ||
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Record in the Search Index
| _version_ | 1807324287389925376 |
|---|---|
| adam_text |
CONTENTS
PART
I
REPRESENTATIONS
AND
CHARACTERS
1
1
GENERALITIES
ON
LINEAR REPRESENTATIONS
3
1.1
DEFINITIONS
3
1.2
BASIC
EXAMPLES
4
1.3
SUBREPRESENTATIONS
5
1.4
IRREDUCIBLE
REPRESENTATIONS
7
1.5
TENSOR
PRODUCT
OF
TWO
REPRESENTATIONS
7
1.6
SYMMETRIE
SQUARE
AND
ALTEMATING
SQUARE
9
2
CHARACTER
THEORY
10
2.1
THE
CHARACTER
OF
A
REPRESENTATION
10
2.2
SCHUR
'
S
LEMMA;
BASIC
APPLICATIONS
13
2.3
ORTHOGONALITY
RELATIONS
FOR
CHARACTERS
15
2.4
DECOMPOSITION
OF
THE
REGULAER
REPRESENTATION
17
2.5
NUMBER
OF
IRREDUCIBLE
REPRESENTATIONS
18
2.6
CANONICAL
DECOMPOSITION
OF
A
REPRESENTATION
21
2.7
EXPLICIT
DECOMPOSITION
OF
A
REPRESENTATION
23
3
SUBGROUPS,
PRODUCTS,
INDUCED
REPRESENTATIONS
25
3.1
ABELIAN
SUBGROUPS
25
3.2
PRODUCT
OF
TWO
GROUPS
26
3.3
INDUCED
REPRESENTATIONS
28
4
COMPACT
GROUPS
32
4.1
COMPACT
GROUPS
32
4.2
INVARIANT
MEASURE
ON
A
COMPACT
GROUP
32
4.3
LINEAR
REPRESENTATIONS
OF
COMPACT
GROUPS
33
VII
CONTENTS
5
EXAMPLES
35
5.1
THE
CYCLIC
GROUP
CYY
35
5.2
THE
GROUP
CYY
36
5.3
THE
DIHEDRAL
GROUP
DYY
36
5.4
THE
GROUP
38
5.5
THE
GROUP
DYY
39
5.6
THE
GROUP
D*
40
5.7
THE
ALTERNATING
GROUP
SI
4
41
5.8
THE
SYMMETRIE
GROUP
OE
4
42
5.9
THE
GROUP
OF
THE
CUBE
43
BIBLIOGRAPHY:
PART
I
44
PART
II
REPRESENTATIONS
IN
CHARACTERISTIC
ZERO
45
6
THE
GROUP
ALGEBRA
47
6.1
REPRESENTATIONS
AND
MODULES
47
6.2
DECOMPOSITION
OF
C[G]
48
6.3
THE
CENTER
OF
C[G
]
50
6.4
BASIC
PROPERTIES
OF
INTEGERS
50
6.5
INTEGRALITY
PROPERTIES
OF
CHARACTERS.
APPLICATIONS
52
7
INDUCED
REPRESENTATIONS;
MACKEY
'
S
CRITERION
54
7.1
INDUCTION
54
7.2
THE
CHARACTER
OF
AN
INDUCED
REPRESENTATION;
55
THE
RECIPROCITY
FORMULA
7.3
RESTRICTION
TO
SUBGROUPS
58
7.4
MACKEY
'
S
IRREDUCIBILITY
CRITERION
59
8
EXAMPLES
OF
INDUCED
REPRESENTATIONS
61
8.1
NORMAL
SUBGROUPS;
APPLICATIONS
TO
THE
DEGREES
OF
THE
61
IRREDUCIBLE
REPRESENTATIONS
8.2
SEMIDIRECT
PRODUCTS
BY
AN
ABELIAN
GROUP
62
8.3
A
REVIEW
OF
SOME
CLASSES
OF
FINITE
GROUPS
63
8.4
SYLOW
'S
THEOREM
65
8.5
LINEAR
REPRESENTATIONS
OF
SUPERSOLVABLE
GROUPS
66
9
ARTIN
'
S
THEOREM
68
9.1
THE
RING
R(G)
68
9.2
STATEMENT
OF
ARTIN
'S
THEOREM
70
9.3
FIRST
PROOF
70
9.4
SECOND
PROOF
OF
(I)
=
(II)
72
10
A
THEOREM
OF
BRAUER
74
10.1
P-REGULAR
ELEMENTS;
P-ELEMENTARY
SUBGROUPS
74
10.2
INDUCED
CHARACTERS
ARISING
FROM
P-ELEMENTARY
75
SUBGROUPS
10.3
CONSTRUCTION
OF
CHARACTERS
76
10.4
PROOF
OF
THEOREMS
18
AND
18'
78
10.5
BRAUER
'
S
THEOREM
78
VIII
CONTENTS
11
APPLICATIONS
OF
BRAUER
'
S
THEOREM
81
11.1
CHARACTERIZATION
OF
CHARACTERS
81
11.2
A
THEOREM
OF
FROBENIUS
83
11.3
A
CONVERSE
TO
BRAUER
'
S
THEOREM
85
11.4
THE
SPECTRUM
OF
A
(X)
R(G)
86
12
RATIONALITY
QUESTIONS
90
12.1
THE
RINGS
R
K
(G)
AND
R
K
(G)
90
12.2
SCHUR
INDICES
92
12.3
REALIZABILITY
OVER
CYCLOTOMIC
FIELDS
94
12.4
THE
RANK
OFR
K
(G)
95
12.5
GENERALIZATION
OF
ARTIN
'
S
THEOREM
96
12.6
GENERALIZATION
OF
BRAUER
'
S
THEOREM
97
12.7
PROOF
OF
THEOREM
28
99
13
RATIONALITY
QUESTIONS:
EXAMPLES
102
13.1
THE
FIELD
Q
102
13.2
THE
FIELD
R
106
BIBLIOGRAPHY:
PART
II
111
PART
III
INTRODUCTION
TO
BRAUER
THEORY
113
14
THE
GROUPS
R
K
(G),
RFC(G),
AND
PFC(G)
115
14.1
THE
RINGS
R
K
(G)
AND
R*(G)
115
14.2
THE
GROUPS
P*(G)
AND
P
A
(G)
116
14.3
STRUCTURE
OF
PFC(G)
116
14.4 STRUCTURE
OF
P
A
(G)
118
14.5
DUALITIES
120
14.6
SCALAR
EXTENSIONS
122
15
THE
CDE
TRIANGLE
124
15.1
DEFINITION
OF
C:
P*(G)
-*
R)T(G)
124
15.2
DEFINITION
OF
D\
R
K
(G)
-
R*(G)
125
15.3
DEFINITION
OF
E:
P
FC
(G)
-
R
K
(G)
127
15.4
BASIC
PROPERTIES
OF
THE
CDE
TRIANGLE
127
15.5
EXAMPLE:
P'-GROUPS
128
15.6
EXAMPLE:
P-GROUPS
129
15.7
EXAMPLE:
PRODUCTS
OFP'-GROUPS
AND
P-GROUPS
129
16
THEOREMS
131
16.1
PROPERTIES
OF
THE
CDE
TRIANGLE
131
16.2
CHARACTERIZATION
OF
THE
IMAGE
OF
E
133
16.3
CHARACTERIZATION
OF
PROJECTIVE
A
[G]-MODULES
134
BY
THEIR
CHARACTERS
16.4
EXAMPLES
OF
PROJECTIVE
A
[G]-MODULES:
IRREDUCIBLE
136
REPRESENTATIONS
OF
DEFECT
ZERO
IX
CONTENTS
17
PROOFS
138
17.1
CHANGE
OF
GROUPS
138
17.2
BRAUER
'
S
THEOREM
IN
THE
MODULAR
CASE
139
17.3
PROOF
OF
THEOREM
33
140
17.4
PROOF
OF
THEOREM
35
142
17.5
PROOF
OF
THEOREM
37
143
17.6
PROOF
OF
THEOREM
38
144
18
MODULAR
CHARACTERS
147
18.1
THE
MODULAR
CHARACTER
OF
A
REPRESENTATION
147
18.2
INDEPENDENCE
OF
MODULAR
CHARACTERS
149
18.3
REFORMULATIONS
151
18.4
A
SECTION
FORD
152
18.5
EXAMPLE:
MODULAR
CHARACTERS
OF
THE
SYMMETRIE
GROUP
153
18.6
EXAMPLE:
MODULAR
CHARACTERS
OF
THE
ALTEMATING
GROUP
2I
5
156
19
APPLICATION
TO
ARTIN
REPRESENTATIONS
159
19.1
ARTIN
AND
SWAN
REPRESENTATIONS
159
19.2
RATIONALITY
OF
THE
ARTIN
AND
SWAN
REPRESENTATIONS
161
19.3
AN
INVARIANT
162
APPENDIX
163
BIBLIOGRAPHY:
PART
III
165
INDEX
OF
NOTATION
167
INDEX
OF
TERMINOLOGY
169
X |
| any_adam_object | 1 |
| author | Serre, Jean-Pierre 1926- |
| author_GND | (DE-588)142283126 |
| author_facet | Serre, Jean-Pierre 1926- |
| author_role | aut |
| author_sort | Serre, Jean-Pierre 1926- |
| author_variant | j p s jps |
| building | Verbundindex |
| bvnumber | BV009843843 |
| callnumber-first | Q - Science |
| callnumber-label | QA177 |
| callnumber-raw | QA177 |
| callnumber-search | QA177 |
| callnumber-sort | QA 3177 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 260 |
| classification_tum | MAT 203f MAT 202f |
| ctrlnum | (OCoLC)29617400 (DE-599)BVBBV009843843 |
| dewey-full | 512/.2 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
| dewey-raw | 512/.2 |
| dewey-search | 512/.2 |
| dewey-sort | 3512 12 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | Corr. 4. pr. |
| format | Book |
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| id | DE-604.BV009843843 |
| illustrated | Illustrated |
| indexdate | 2024-08-14T01:25:53Z |
| institution | BVB |
| isbn | 3540901906 0387901906 |
| language | English French |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-006518305 |
| oclc_num | 29617400 |
| open_access_boolean | |
| owner | DE-91 DE-BY-TUM DE-83 DE-11 DE-188 DE-91G DE-BY-TUM |
| owner_facet | DE-91 DE-BY-TUM DE-83 DE-11 DE-188 DE-91G DE-BY-TUM |
| physical | X, 170 S. graph. Darst. |
| publishDate | 1993 |
| publishDateSearch | 1993 |
| publishDateSort | 1993 |
| publisher | Springer |
| record_format | marc |
| series | Graduate texts in mathematics |
| series2 | Graduate texts in mathematics |
| spelling | Serre, Jean-Pierre 1926- Verfasser (DE-588)142283126 aut Représentations linéaires des groupes finis Linear representations of finite groups Jean-Pierre Serre. Transl. from the French by Leonard L. Scott Corr. 4. pr. New York ; Berlin ; Heidelberg ; London ; Paris ; Tokyo ; Hong K Springer 1993 X, 170 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Graduate texts in mathematics 42 Literaturangaben Finite groups Representations of groups Endliche Gruppe (DE-588)4014651-0 gnd rswk-swf Gruppentheorie (DE-588)4072157-7 gnd rswk-swf Lineare Darstellung (DE-588)4167703-1 gnd rswk-swf Darstellungstheorie (DE-588)4148816-7 gnd rswk-swf Endliche Gruppe (DE-588)4014651-0 s Lineare Darstellung (DE-588)4167703-1 s DE-604 Darstellungstheorie (DE-588)4148816-7 s 1\p DE-604 Gruppentheorie (DE-588)4072157-7 s 2\p DE-604 Graduate texts in mathematics 42 (DE-604)BV000000067 42 DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006518305&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Serre, Jean-Pierre 1926- Linear representations of finite groups Graduate texts in mathematics Finite groups Representations of groups Endliche Gruppe (DE-588)4014651-0 gnd Gruppentheorie (DE-588)4072157-7 gnd Lineare Darstellung (DE-588)4167703-1 gnd Darstellungstheorie (DE-588)4148816-7 gnd |
| subject_GND | (DE-588)4014651-0 (DE-588)4072157-7 (DE-588)4167703-1 (DE-588)4148816-7 |
| title | Linear representations of finite groups |
| title_alt | Représentations linéaires des groupes finis |
| title_auth | Linear representations of finite groups |
| title_exact_search | Linear representations of finite groups |
| title_full | Linear representations of finite groups Jean-Pierre Serre. Transl. from the French by Leonard L. Scott |
| title_fullStr | Linear representations of finite groups Jean-Pierre Serre. Transl. from the French by Leonard L. Scott |
| title_full_unstemmed | Linear representations of finite groups Jean-Pierre Serre. Transl. from the French by Leonard L. Scott |
| title_short | Linear representations of finite groups |
| title_sort | linear representations of finite groups |
| topic | Finite groups Representations of groups Endliche Gruppe (DE-588)4014651-0 gnd Gruppentheorie (DE-588)4072157-7 gnd Lineare Darstellung (DE-588)4167703-1 gnd Darstellungstheorie (DE-588)4148816-7 gnd |
| topic_facet | Finite groups Representations of groups Endliche Gruppe Gruppentheorie Lineare Darstellung Darstellungstheorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006518305&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000000067 |
| work_keys_str_mv | AT serrejeanpierre representationslineairesdesgroupesfinis AT serrejeanpierre linearrepresentationsoffinitegroups |