Linear algebraic groups:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | German |
| Veröffentlicht: |
New York ; Berlin ; Heidelberg ; London ; Paris ; Tokyo ; Hong K
Springer
1995
|
| Ausgabe: | (Corr. 4. printing) |
| Schriftenreihe: | Graduate texts in mathematics
21 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Literaturverz. S. 233 - 245 |
| Beschreibung: | XVI, 253 S. |
| ISBN: | 3540901086 0387901086 |
Internformat
MARC
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| 084 | |a MAT 204f |2 stub | ||
| 100 | 1 | |a Humphreys, James E. |d 1939-2020 |e Verfasser |0 (DE-588)108120848 |4 aut | |
| 245 | 1 | 0 | |a Linear algebraic groups |c James E. Humphreys |
| 250 | |a (Corr. 4. printing) | ||
| 264 | 1 | |a New York ; Berlin ; Heidelberg ; London ; Paris ; Tokyo ; Hong K |b Springer |c 1995 | |
| 300 | |a XVI, 253 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a Graduate texts in mathematics |v 21 | |
| 500 | |a Literaturverz. S. 233 - 245 | ||
| 650 | 4 | |a Linear algebraic groups | |
| 650 | 0 | 7 | |a Lineare Gruppe |0 (DE-588)4138778-8 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Lineare algebraische Gruppe |0 (DE-588)4295326-1 |2 gnd |9 rswk-swf |
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| 650 | 0 | 7 | |a Algebraische Gruppe |0 (DE-588)4001164-1 |2 gnd |9 rswk-swf |
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Datensatz im Suchindex
| _version_ | 1807323859118981120 |
|---|---|
| adam_text |
TABLE
OF
CONTENTS
I.
ALGEBRAIC
GEOMETRY
1
0.
SOME
COMMUTATIVE
ALGEBRA
.
1
1.
AFFINE
AND
PROJECTIVE
VARIETIES
.
4
1.1
IDEALS
AND
AFFINE
VARIETIES
.
4
1.2
ZARISKI
TOPOLOGY
ON
AFFINE
SPACE
.
6
1.3
IRREDUCIBLE
COMPONENTS
.
7
1.4
PRODUCTS
OF
AFFINE
VARIETIES
.
9
1.5
AFFINE
ALGEBRAS
AND
MORPHISMS
.
9
1.6
PROJECTIVE
VARIETIES
.
.
.
.
.
.
.
11
1.7
PRODUCTS
OF
PROJECTIVE
VARIETIES
.
13
1.8
FLAG
VARIETIES
.
14
2.
VARIETIES
.
16
2.1
LOCAL
RINGS
.
16
2.2
PREVARIETIES
.
.
.
17
2.3
MORPHISMS
.
18
2.4
PRODUCTS
.
20
2.5
HAUSDORFF
AXIOM
.
22
3.
DIMENSION
.
24
3.1
DIMENSION
OF
A
VARIETY
.
24
3.2
DIMENSION
OF
A
SUBVARIETY
.
25
3.3
DIMENSION
THEOREM
.
26
3.4
CONSEQUENCES
.
28
4.
MORPHISMS
.
29
4.1
FIBRES
OF
A
MORPHISM
.
29
4.2
FINITE
MORPHISMS
.
31
4.3
IMAGE
OF
A
MORPHISM
.
32
4.4
CONSTRUCTIBLE
SETS
.
33
4.5
OPEN
MORPHISMS
.
34
4.6
BIJECTIVE
MORPHISMS
.
34
4.7
BIRATIONAL
MORPHISMS
.
36
5.
TANGENT
SPACES
.
37
5.1
ZARISKI
TANGENT
SPACE
.
37
5.2
EXISTENCE
OF
SIMPLE
POINTS
.
39
5.3
LOCAL
RING
OF
A
SIMPLE
POINT
.
40
5.4
DIFFERENTIAL
OF
A
MORPHISM
.
42
5.5
DIFFERENTIAL
CRITERION
FOR
SEPARABILITY
.
43
XII
TABLE
OF
CONTENTS
6.
COMPLETE
VARIETIES
.
45
6.1
BASIC
PROPERTIES
.
45
6.2
COMPLETENESS
OF
PROJECTIVE
VARIETIES
.
46
6.3
VARIETIES
ISOMORPHIC
TO
P
1
.
47
6.4
AUTOMORPHISMS
OF
P
1
.
47
II.
AFFINE
ALGEBRAIC
GROUPS
51
7.
BASIC
CONCEPTS
AND
EXAMPLES
.
51
7.1
THE
NOTION
OF
ALGEBRAIC
GROUP
.
51
7.2
SOME
CLASSICAL
GROUPS
.
52
7.3
IDENTITY
COMPONENT
.
.
.
.
.
.
.53
7.4
SUBGROUPS
AND
HOMOMORPHISMS
.
54
7.5
GENERATION
BY
IRREDUCIBLE
SUBSETS
.
55
7.6
HOPF
ALGEBRAS
.
56
8.
ACTIONS
OF
ALGEBRAIC
GROUPS
ON
VARIETIES
.
58
8.1
GROUP
ACTIONS
.
58
8.2
ACTIONS
OF
ALGEBRAIC
GROUPS
.
59
8.3
CLOSED
ORBITS
.
60
8.4
SEMIDIRECT
PRODUCTS
.
61
8.5
TRANSLATION
OF
FUNCTIONS
.
61
8.6
LINEARIZATION
OF
AFFINE
GROUPS
.
62
III.
LIE
ALGEBRAS
65
9.
LIE
ALGEBRA
OF
AN
ALGEBRAIC
GROUP
.
65
9.1
LIE
ALGEBRAS
AND
TANGENT
SPACES
.
65
9.2
CONVOLUTION
.
66
9.3
EXAMPLES
.
67
9.4
SUBGROUPS
AND
LIE
SUBALGEBRAS
.
68
9.5
DUAL
NUMBERS
.
69
10.
DIFFERENTIATION
.
70
10.1
SOME
ELEMENTARY
FORMULAS
.
71
10.2
DIFFERENTIAL
OF
RIGHT
TRANSLATION
.
.
.
71
10.3
THE
ADJOINT
REPRESENTATION
.
72
10.4
DIFFERENTIAL
OF
AD
.
73
10.5
COMMUTATORS
.
75
10.6
CENTRALIZERS
.
76
10.7
AUTOMORPHISMS
AND
DERIVATIONS
.
76
IV.
HOMOGENEOUS
SPACES
79
11.
CONSTRUCTION
OF
CERTAIN
REPRESENTATIONS
.
79
11.1
ACTION
ON
EXTERIOR
POWERS
.
79
11.2
A
THEOREM
OF
CHEVALLEY
.
80
11.3
PASSAGE
TO
PROJECTIVE
SPACE
.
80
TABLE
OF
CONTENTS
XIII
11.4
CHARACTERS
AND
SEMI-INVARIANTS
.
81
11.5
NORMAL
SUBGROUPS
.
82
12.
QUOTIENTS
.
83
12.1
UNIVERSAL
MAPPING
PROPERTY
.
83
12.2
TOPOLOGY
OF
Y
.
84
12.3
FUNCTIONS
ON
Y
.
.
.
.
.
.84
12.4
COMPLEMENTS
.
85
12.5
CHARACTERISTIC
0
.
85
V.
CHARACTERISTIC
0
THEORY
87
13.
CORRESPONDENCE
BETWEEN
GROUPS
AND
LIE
ALGEBRAS
.
87
13.1
THE
LATTICE
CORRESPONDENCE
.
87
13.2
INVARIANTS
AND
INVARIANT
SUBSPACES
.
88
13.3
NORMAL
SUBGROUPS
AND
IDEALS
.
88
13.4
CENTERS
AND
CENTRALIZERS
.
89
13.5
SEMISIMPLE
GROUPS
AND
LIE
ALGEBRAS
.
.
89
14.
SEMISIMPLE
GROUPS
.
90
14.1
THE
ADJOINT
REPRESENTATION
.
90
14.2
SUBGROUPS
OF
A
SEMISIMPLE
GROUP
.
91
14.3
COMPLETE
REDUCIBILITY
OF
REPRESENTATIONS
.
92
VI.
SEMISIMPLE
AND
UNIPOTENT
ELEMENTS
95
15.
JORDAN-CHEVALLEY
DECOMPOSITION
.
95
15.1
DECOMPOSITION
OF
A
SINGLE
ENDOMORPHISM
.
.
.
95
15.2
GL(,
K)
AND
GL(N,
K)
.
97
15.3
JORDAN
DECOMPOSITION
IN
ALGEBRAIC
GROUPS
.
.
98
15.4
COMMUTING
SETS
OF
ENDOMORPHISMS
.
99
15.5
STRUCTURE
OF
COMMUTATIVE
ALGEBRAIC
GROUPS
100
16.
DIAGONALIZABLE
GROUPS
.
101
16.1
CHARACTERS
AND
D-GROUPS
.
101
16.2
TORI
.
103
16.3
RIGIDITY
OF
DIAGONALIZABLE
GROUPS
.
.
.105
16.4
WEIGHTS
AND
ROOTS
.
.
.
.
.
.106
VII.
SOLVABLE
GROUPS
109
17.
NILPOTENT
AND
SOLVABLE
GROUPS
.
109
17.1
A
GROUP-THEORETIC
LEMMA
.
.
.109
17.2
COMMUTATOR
GROUPS
.
110
17.3
SOLVABLE
GROUPS
.
110
17.4
NILPOTENT
GROUPS
.
.
.
.
.
.ILL
17.5
UNIPOTENT
GROUPS
.
.
.
.
.112
17.6
LIE-KOLCHIN
THEOREM
.
.
.
.
.
.113
XIV
TABLE
OF
CONTENTS
18.
SEMISIMPLE
ELEMENTS
.
.
.
.
.
.
.
.115
18.1
GLOBAL
AND
INFINITESIMAL
CENTRALIZERS
.
.
.
116
18.2
CLOSED
CONJUGACY
CLASSES
.
.
.
.
.
.117
18.3
ACTION
OF
A
SEMISIMPLE
ELEMENT
ON
A
UNIPOTENT
GROUP
118
18.4
ACTION
OF
A
DIAGONALIZABLE
GROUP
.
.
119
19.
CONNECTED
SOLVABLE
GROUPS
.
121
19.1
AN
EXACT
SEQUENCE
.
.
.
.
.
.
.122
19.2
THE
NILPOTENT
CASE
.
.
.
.
.122
19.3
THE
GENERAL
CASE
.
123
19.4
NORMALIZER
AND
CENTRALIZER
.
124
19.5
SOLVABLE
AND
UNIPOTENT
RADICALS
.
.
.125
20.
ONE
DIMENSIONAL
GROUPS
.
126
20.1
COMMUTATIVITY
OF
G
.
126
20.2
VECTOR
GROUPS
AND
E-GROUPS
.
127
20.3
PROPERTIES
OF
/^-POLYNOMIALS
.
.
.
.
.128
20.4
AUTOMORPHISMS
OF
VECTOR
GROUPS
.
.
.130
20.5
THE
MAIN
THEOREM
.
.
.
.
.131
VIII.
BOREL
SUBGROUPS
133
21.
FIXED
POINT
AND
CONJUGACY
THEOREMS
.
.
.
.
.133
21.1
REVIEW
OF
COMPLETE
VARIETIES
.
.
.
.
.133
21.2
FIXED
POINT
THEOREM
.
.134
21.3
CONJUGACY
OF
BOREL
SUBGROUPS
AND
MAXIMAL
TORI
.
134
21.4
FURTHER
CONSEQUENCES
.
136
22.
DENSITY
AND
CONNECTEDNESS
THEOREMS
.
138
22.1
THE
MAIN
LEMMA
.
138
22.2
DENSITY
THEOREM
.
.
.
.
.139
22.3
CONNECTEDNESS
THEOREM
.
140
22.4
BOREL
SUBGROUPS
OF
C
G
(S)
.
141
22.5
CARTAN
SUBGROUPS
:
SUMMARY
.
142
23.
NORMALIZER
THEOREM
.
.
.
.
.
.143
23.1
STATEMENT
OF
THE
THEOREM
.
143
23.2
PROOF
OF
THE
THEOREM
.
144
23.3
THE
VARIETY
G/5
.
145
23.4
SUMMARY
.
145
IX.
CENTRALIZERS
OF
TORI
147
24.
REGULAR
AND
SINGULAR
TORI
.
.
.
.
.147
24.1
WEYL
GROUPS
.
147
24.2
REGULAR
TORI
.
149
24.3
SINGULAR
TORI
AND
ROOTS
.
149
24.4
REGULAR
1
-PARAMETER
SUBGROUPS
.150
TABLE
OF
CONTENTS
XV
25.
ACTION
OF
A
MAXIMAL
TORUS
ON
GFB
.
151
25.1
ACTION
OF
A
1
-PARAMETER
SUBGROUP
.
.
.152
25.2
EXISTENCE
OF
ENOUGH
FIXED
POINTS
.
.
.
.153
25.3
GROUPS
OF
SEMISIMPLE
RANK
1
.
.
.
.
.154
25.4
WEYL
CHAMBERS
.
156
26.
THE
UNIPOTENT
RADICAL
.
.
.
.
.
.157
26.1
CHARACTERIZATION
OF
R
U
(G)
.
158
26.2
SOME
CONSEQUENCES
.
.
.
.
.
.159
26.3
THE
GROUPS
UYY
.
160
X.
STRUCTURE
OF
REDUCTIVE
GROUPS
163
27.
THE
ROOT
SYSTEM
.
.
.
.
.163
27.1
ABSTRACT
ROOT
SYSTEMS
.
163
27.2
THE
INTEGRALITY
AXIOM
.
164
27.3
SIMPLE
ROOTS
.
165
27.4
THE
AUTOMORPHISM
GROUP
OF
A
SEMISIMPLE
GROUP
.
166
27.5
SIMPLE
COMPONENTS
.
.
.
.
.
.167
28.
BRUHAT
DECOMPOSITION
.
169
28.1
T-STABLE
SUBGROUPS
OF
B
U
.
169
28.2
GROUPS
OF
SEMISIMPLE
RANK
1
.
171
28.3
THE
BRUHAT
DECOMPOSITION
.
.
.172
28.4
NORMAL
FORM
IN
G
.
173
28.5
COMPLEMENTS
.
173
29.
TITS
SYSTEMS
.
175
29.1
AXIOMS
.
176
29.2
BRUHAT
DECOMPOSITION
.
177
29.3
PARABOLIC
SUBGROUPS
.
177
29.4
GENERATORS
AND
RELATIONS
FOR
IF
.
.
.179
29.5
NORMAL
SUBGROUPS
OF
G
.
181
30.
PARABOLIC
SUBGROUPS
.
183
30.1
STANDARD
PARABOLIC
SUBGROUPS
.
.
.
.
.183
30.2
LEVI
DECOMPOSITIONS
.
184
30.3
PARABOLIC
SUBGROUPS
ASSOCIATED
TO
CERTAIN
UNIPOTENT
GROUPS
.
185
30.4
MAXIMAL
SUBGROUPS
AND
MAXIMAL
UNIPOTENT
SUBGROUPS
187
XI.
REPRESENTATIONS
AND
CLASSIFICATION
OF
SEMISIMPLE
GROUPS
188
31.
REPRESENTATIONS
.
.
.
.
.
.188
31.1
WEIGHTS
.
188
31.2
MAXIMAL
VECTORS
.
189
31.3
IRREDUCIBLE
REPRESENTATIONS
.190
31.4
CONSTRUCTION
OF
IRREDUCIBLE
REPRESENTATIONS
.
.
191
XVI
TABLE
OF
CONTENTS
31.5
MULTIPLICITIES
AND
MINIMAL
HIGHEST
WEIGHTS
.
.
193
31.6
CONTRAGREDIENTS
AND
INVARIANT
BILINEAR
FORMS
.
.
193
32.
ISOMORPHISM
THEOREM
.
195
32.1
THE
CLASSIFICATION
PROBLEM
.
195
32.2
EXTENSION
OF
P
T
TO
N(T)
.
198
32.3
EXTENSION
OF
P
T
TO
Z
A
.
199
32.4
EXTENSION
OF
P
T
TO
TU
A
.
201
32.5
EXTENSION
OF
(P
T
TO
B
.
203
32.6
MULTIPLICATIVITY
OF
.
204
33.
ROOT
SYSTEMS
OF
RANK
2
.
207
33.1
REFORMULATION
OF
(A),
(B),
(C)
.
207
33.2
SOME
PRELIMINARIES
.
208
33.3
TYPE
A
2
.
209
33.4
TYPE
B
2
.
211
33.5
TYPEG
2
.
212
33.6
THE
EXISTENCE
PROBLEM
.
215
XII.
SURVEY
OF
RATIONALITY
PROPERTIES
217
34.
FIELDS
OF
DEFINITION
.
.
.
.
.
.
.217
34.1
FOUNDATIONS
.
217
34.2
REVIEW
OF
EARLIER
CHAPTERS
.
218
34.3
TORI
YY
.
219
34.4
SOME
BASIC
THEOREMS
.
219
34.5
BOREL-TITS
STRUCTURE
THEORY
.
220
34.6
AN
EXAMPLE:
ORTHOGONAL
GROUPS
.
.
.
.221
35.
SPECIAL
CASES
.
222
35.1
SPLIT
AND
QUASISPLIT
GROUPS
.
223
35.2
FINITE
FIELDS
.
224
35.3
THE
REAL
FIELD
.
224
35.4
LOCAL
FIELDS
.
225
35.5
CLASSIFICATION
.
226
APPENDIX.
ROOT
SYSTEMS
.
229
BIBLIOGRAPHY
.
233
INDEX
OF
TERMINOLOGY
.
247
INDEX
OF
SYMBOLS
.
251 |
| any_adam_object | 1 |
| author | Humphreys, James E. 1939-2020 |
| author_GND | (DE-588)108120848 |
| author_facet | Humphreys, James E. 1939-2020 |
| author_role | aut |
| author_sort | Humphreys, James E. 1939-2020 |
| author_variant | j e h je jeh |
| building | Verbundindex |
| bvnumber | BV010387552 |
| callnumber-first | Q - Science |
| callnumber-label | QA179 |
| callnumber-raw | QA179 |
| callnumber-search | QA179 |
| callnumber-sort | QA 3179 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | QH 140 SK 240 SK 260 |
| classification_tum | MAT 204f |
| ctrlnum | (OCoLC)7718938 (DE-599)BVBBV010387552 |
| 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 Wirtschaftswissenschaften |
| edition | (Corr. 4. printing) |
| format | Book |
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| id | DE-604.BV010387552 |
| illustrated | Not Illustrated |
| indexdate | 2024-08-14T01:19:03Z |
| institution | BVB |
| isbn | 3540901086 0387901086 |
| language | German |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-006916508 |
| oclc_num | 7718938 |
| open_access_boolean | |
| owner | DE-91 DE-BY-TUM DE-11 |
| owner_facet | DE-91 DE-BY-TUM DE-11 |
| physical | XVI, 253 S. |
| publishDate | 1995 |
| publishDateSearch | 1995 |
| publishDateSort | 1995 |
| publisher | Springer |
| record_format | marc |
| series2 | Graduate texts in mathematics |
| spelling | Humphreys, James E. 1939-2020 Verfasser (DE-588)108120848 aut Linear algebraic groups James E. Humphreys (Corr. 4. printing) New York ; Berlin ; Heidelberg ; London ; Paris ; Tokyo ; Hong K Springer 1995 XVI, 253 S. txt rdacontent n rdamedia nc rdacarrier Graduate texts in mathematics 21 Literaturverz. S. 233 - 245 Linear algebraic groups Lineare Gruppe (DE-588)4138778-8 gnd rswk-swf Lineare algebraische Gruppe (DE-588)4295326-1 gnd rswk-swf Lie-Algebra (DE-588)4130355-6 gnd rswk-swf Algebraische Gruppe (DE-588)4001164-1 gnd rswk-swf Lineare algebraische Gruppe (DE-588)4295326-1 s DE-604 Algebraische Gruppe (DE-588)4001164-1 s 1\p DE-604 Lie-Algebra (DE-588)4130355-6 s 2\p DE-604 Lineare Gruppe (DE-588)4138778-8 s 3\p DE-604 DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006916508&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 3\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Humphreys, James E. 1939-2020 Linear algebraic groups Linear algebraic groups Lineare Gruppe (DE-588)4138778-8 gnd Lineare algebraische Gruppe (DE-588)4295326-1 gnd Lie-Algebra (DE-588)4130355-6 gnd Algebraische Gruppe (DE-588)4001164-1 gnd |
| subject_GND | (DE-588)4138778-8 (DE-588)4295326-1 (DE-588)4130355-6 (DE-588)4001164-1 |
| title | Linear algebraic groups |
| title_auth | Linear algebraic groups |
| title_exact_search | Linear algebraic groups |
| title_full | Linear algebraic groups James E. Humphreys |
| title_fullStr | Linear algebraic groups James E. Humphreys |
| title_full_unstemmed | Linear algebraic groups James E. Humphreys |
| title_short | Linear algebraic groups |
| title_sort | linear algebraic groups |
| topic | Linear algebraic groups Lineare Gruppe (DE-588)4138778-8 gnd Lineare algebraische Gruppe (DE-588)4295326-1 gnd Lie-Algebra (DE-588)4130355-6 gnd Algebraische Gruppe (DE-588)4001164-1 gnd |
| topic_facet | Linear algebraic groups Lineare Gruppe Lineare algebraische Gruppe Lie-Algebra Algebraische Gruppe |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006916508&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT humphreysjamese linearalgebraicgroups |