Lie algebras and Lie groups: 1964 lectures given at Harvard University
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin [u.a.]
Springer
2006
|
| Edition: | 2. ed., corr. 5. print. |
| Series: | Lecture notes in mathematics
1500 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | VII, 168 S. |
| ISBN: | 3540550089 |
Staff View
MARC
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| 100 | 1 | |a Serre, Jean-Pierre |d 1926- |e Verfasser |0 (DE-588)142283126 |4 aut | |
| 245 | 1 | 0 | |a Lie algebras and Lie groups |b 1964 lectures given at Harvard University |c Jean-Pierre Serre |
| 250 | |a 2. ed., corr. 5. print. | ||
| 264 | 1 | |a Berlin [u.a.] |b Springer |c 2006 | |
| 300 | |a VII, 168 S. | ||
| 336 | |b txt |2 rdacontent | ||
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| 490 | 1 | |a Lecture notes in mathematics |v 1500 | |
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Record in the Search Index
| _version_ | 1804142541948321792 |
|---|---|
| adam_text | Contents
Part I
-
Lie Algebras
................................................ 1
Introduction
........................................................... 1
Chapter I. Lie Algebras: Definition and Examples
....................... 2
Chapter II. Filtered Groups and Lie Algebras
........................... 6
1.
Formulae on commutators
........................................ 6
2.
Filtration on a group
............................................. 7
3.
Integral nitrations of a group
..................................... 8
4.
Filtrations in GL(n)
.............................................. 9
Exercises
.......................................................... 10
Chapter III. Universal Algebra of a Lie Algebra
........................ 11
1.
Definition
....................................................... 11
2.
Functorial properties
............................................ 12
3.
Symmetric algebra of a module
.................................. 12
4.
Filtration of
U
g.................................................
13
5.
Diagonal map
................................................... 16
Exercises
.......................................................... 17
Chapter IV. Free Lie Algebras
......................................... 18
1.
Free magmas
.................................................... 18
2.
Free algebra on X
............................................... 18
3.
Free Lie algebra on X
........................................... 19
4.
Relation with the free associative algebra on X
.................. 20
5.
P. Hall families
.................................................. 22
6.
Free groups
..................................................... 24
7.
The Campbell-Hausdorff formula
..............................., 26
8.
Explicit formula
................................................. 28
Exercises
.......................................................... 29
Chapter V.
Nilpotent
and Solvable Lie Algebras
....................... 31
1.
Complements on ¿-modules
..................................... 31
2.
Nilpotent Lie algebras
........................................... 32
3.
Main theorems
.....................................·.........■ · ■ 33
3*.
The group-theoretic analog of Engel s theorem
.................. 35
4.
Solvable Lie algebras
............................................ 35
Vi
Contents
5.
Main theorem
................................................... 36
5*.
The group theoretic analog of Lie s theorem
.................... 38
6.
Lemmas on endomorphisms
..................................... 40
7.
Cartan s criterion
............................................... 42
Exercises
.......................................................... 43
Chapter VI.
Semisimple
Lie Algebras
.................................. 44
1.
The radical
..................................................... 44
2. Semisimple
Lie algebras
......................................... 44
3.
Complete reducibility
........................................... 45
4.
Levi s theorem
.................................................. 48
5.
Complete reducibility continued
................................. 50
6.
Connection with compact Lie groups over
R
and
С
.............. 53
Exercises
.......................................................... 54
Chapter
VII.
Representations of
*(„ ................................... 56
1.
Notations
....................................................... 56
2.
Weights and primitive elements
................................. 57
3.
Irreducible ^-modules
........................................... 58
4.
Determination of the highest weights
............................ 59
Exercises
.......................................................... 61
Part II
-
Lie Groups
............................................... 63
Introduction
.......................................................... 63
Chapter I. Complete Fields
............................................ 64
Chapter II. Analytic Functions
........................................ 67
Tournants dangereux
............................................ 75
Chapter III. Analytic Manifolds
....................................... 76
1.
Charts and atlases
.............................................. 76
2.
Definition of analytic manifolds
................................. 77
3.
Topological properties of manifolds
.............................. 77
4.
Elementary examples of manifolds
............................... 78
5.
Morphisms
...................................................... 78
6.
Products and sums
.............................................. 79
7.
Germs of analytic functions
..................................... 80
8.
Tangent and cotangent spaces
................................... 81
9.
Inverse function theorem
........................................ 83
10.
Immersions, submersions, and
subimmersions
................... 83
11.
Construction of manifolds: inverse images
...................... 87
12.
Construction of manifolds: quotients
........................... 92
Exercises
.......................................................... 95
Appendix
1.
A non-regular Hausdorff manifold
.................___ 96
Appendix
2.
Structure of p-adic manifolds
.......................... 97
Appendix
3.
The
transfinite
p-adic line
............................ 101
Contents
vu
Chapter IV. Analytic Groups
......................................... 102
1.
Definition of analytic groups
................................... 102
2.
Elementary examples of analytic groups
........................ 103
3.
Group chunks
.................................................. 105
4.
Prolongation of subgroup chunks
............................... 106
5.
Homogeneous spaces and orbits
................................ 108
6.
Formal groups: definition and elementary examples
.............
Ill
7.
Formal groups: formulae
...............................·........ 113
8.
Formal groups over a complete valuation ring
................... 116
9.
Filtrations on standard groups
................................. 117
Exercises
......................................................... 120
Appendix
1.
Maximal compact subgroups of GL(r», k)
............. 121
Appendix
2.
Some convergence lemmas
........................... 122
Appendix
3.
Applications of
§9:
Filtrations on standard groups
.. 124
Chapter V. Lie Theory
............................................... 129
1.
The Lie algebra of an analytic group chunk
..................... 129
2.
Elementary examples and properties
............................ 130
3.
Linear representations
.......................................... 131
4.
The convergence of the Campbell-Hausdorff formula
............ 136
5.
Point distributions
............................................. 141
6.
The bialgebra associated to a formal group
..................... 143
7.
The convergence of formal homomorphisms
..................... 149
8.
The third theorem of Lie
....................................... 152
9.
Cartan s theorems
............................................. 155
Exercises
......................................................... 157
Appendix. Existence theorem for ordinary differential equations
... 158
Bibliography
....................................................... 161
Problem
............................................................ 163
Index
......................................................... 165
|
| 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 | BV025392324 |
| classification_rvk | SI 850 SK 340 |
| ctrlnum | (OCoLC)636371460 (DE-599)BVBBV025392324 |
| discipline | Mathematik |
| edition | 2. ed., corr. 5. print. |
| format | Book |
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| institution | BVB |
| isbn | 3540550089 |
| language | English |
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| physical | VII, 168 S. |
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| publisher | Springer |
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| series | Lecture notes in mathematics |
| series2 | Lecture notes in mathematics |
| spelling | Serre, Jean-Pierre 1926- Verfasser (DE-588)142283126 aut Lie algebras and Lie groups 1964 lectures given at Harvard University Jean-Pierre Serre 2. ed., corr. 5. print. Berlin [u.a.] Springer 2006 VII, 168 S. txt rdacontent n rdamedia nc rdacarrier Lecture notes in mathematics 1500 Lie-Gruppe (DE-588)4035695-4 gnd rswk-swf Lie-Algebra (DE-588)4130355-6 gnd rswk-swf 1\p (DE-588)1071861417 Konferenzschrift gnd-content Lie-Algebra (DE-588)4130355-6 s DE-604 Lie-Gruppe (DE-588)4035695-4 s Lecture notes in mathematics 1500 (DE-604)BV000676446 1500 Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020015625&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Serre, Jean-Pierre 1926- Lie algebras and Lie groups 1964 lectures given at Harvard University Lecture notes in mathematics Lie-Gruppe (DE-588)4035695-4 gnd Lie-Algebra (DE-588)4130355-6 gnd |
| subject_GND | (DE-588)4035695-4 (DE-588)4130355-6 (DE-588)1071861417 |
| title | Lie algebras and Lie groups 1964 lectures given at Harvard University |
| title_auth | Lie algebras and Lie groups 1964 lectures given at Harvard University |
| title_exact_search | Lie algebras and Lie groups 1964 lectures given at Harvard University |
| title_full | Lie algebras and Lie groups 1964 lectures given at Harvard University Jean-Pierre Serre |
| title_fullStr | Lie algebras and Lie groups 1964 lectures given at Harvard University Jean-Pierre Serre |
| title_full_unstemmed | Lie algebras and Lie groups 1964 lectures given at Harvard University Jean-Pierre Serre |
| title_short | Lie algebras and Lie groups |
| title_sort | lie algebras and lie groups 1964 lectures given at harvard university |
| title_sub | 1964 lectures given at Harvard University |
| topic | Lie-Gruppe (DE-588)4035695-4 gnd Lie-Algebra (DE-588)4130355-6 gnd |
| topic_facet | Lie-Gruppe Lie-Algebra Konferenzschrift |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020015625&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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| work_keys_str_mv | AT serrejeanpierre liealgebrasandliegroups1964lecturesgivenatharvarduniversity |