Lie groups: A problem oriented introduction via matrix groups
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Washington, DC
Mathematical Assoc. of America
2009
|
| Series: | MAA textbooks
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XII, 177 S. |
| ISBN: | 9780883857595 |
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MARC
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| 245 | 1 | 0 | |a Lie groups |b A problem oriented introduction via matrix groups |c Harriet Pollatsek |
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Record in the Search Index
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| adam_text | Contents
Preface
vii
1
Symmetries of vector spaces
1
1.1
What is a symmetry?
........................... 1
1.2
Distance is fundamental
......................... 5
1.3
Groups of symmetries
........................... 8
1.4
Bilinear forms and symmetries of spacetime
............... 14
1.5
Putting the pieces together
........................ 20
1.6
A broader view: Lie groups
....................... 26
2
Complex numbers, quaternions and geometry
29
2.1
Complex numbers
............................. 29
2.2
Quaternions
................................ 33
2.3
The geometry of rotations of R3
..................... 35
2.4
Putting the pieces together
........................ 39
2.5
A broader view: octonions
........................ 41
3
Linearization
45
3.1
Tangent spaces
.............................. 45
3.2
Group homomorphisms
.......................... 51
3.3
Differentials
................................ 55
3.4
Putting the pieces together
........................ 63
3.5
A broader view: Hubert s fifth problem
................. 66
4
One-parameter subgroups and the exponential map
69
4.1
One-parameter subgroups
......................... 69
4.2
The exponential map in dimension
1................... 70
4.3
Calculating the matrix exponential
.................... 72
4.4
Properties of the matrix exponential
................... 76
4.5
Using
exp
to determine L(G)
...................... 78
4.6
Differential equations
........................... 81
4.7
Putting the pieces together
........................ 87
4.8
A broader view: Lie and differential equations
............. 91
4.9
Appendix on convergence
........................ 93
5
Lie algebras
99
5.1
Lie algebras
................................ 99
5.2
Adjoint maps
—
big A and small a
.................. 104
5.3
Putting the pieces together
........................ 108
5.4
A broader view: Lie theory
........................
Ill
6
Matrix groups over other fields
115
6.1
What is a field?
.............................. 115
6.2
The unitary group
............................. 116
6.3
Matrix groups over finite fields
..................... 121
6.4
Putting the pieces together
........................ 127
6.5
A broader view: finite groups of Lie type and simple groups
...... 132
I Linear algebra facts
141
II Paper assignment used at Mount Holyoke College
145
III Opportunities for further study
149
Solutions to selected problems
153
Bibliography
169
Index
171
Notation
175
About the Author
177
|
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| isbn | 9780883857595 |
| language | English |
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| physical | XII, 177 S. |
| publishDate | 2009 |
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| publisher | Mathematical Assoc. of America |
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| series2 | MAA textbooks |
| spelling | Pollatsek, Harriet 1942- Verfasser (DE-588)1043940693 aut Lie groups A problem oriented introduction via matrix groups Harriet Pollatsek Washington, DC Mathematical Assoc. of America 2009 XII, 177 S. txt rdacontent n rdamedia nc rdacarrier MAA textbooks Lie groups Lie groups Problems, exercises, etc Matrix groups Lie-Gruppe (DE-588)4035695-4 gnd rswk-swf Matrizengruppe (DE-588)4169127-1 gnd rswk-swf (DE-588)4143389-0 Aufgabensammlung gnd-content Lie-Gruppe (DE-588)4035695-4 s Matrizengruppe (DE-588)4169127-1 s DE-604 Digitalisierung UB Passau application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018612202&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Pollatsek, Harriet 1942- Lie groups A problem oriented introduction via matrix groups Lie groups Lie groups Problems, exercises, etc Matrix groups Lie-Gruppe (DE-588)4035695-4 gnd Matrizengruppe (DE-588)4169127-1 gnd |
| subject_GND | (DE-588)4035695-4 (DE-588)4169127-1 (DE-588)4143389-0 |
| title | Lie groups A problem oriented introduction via matrix groups |
| title_auth | Lie groups A problem oriented introduction via matrix groups |
| title_exact_search | Lie groups A problem oriented introduction via matrix groups |
| title_full | Lie groups A problem oriented introduction via matrix groups Harriet Pollatsek |
| title_fullStr | Lie groups A problem oriented introduction via matrix groups Harriet Pollatsek |
| title_full_unstemmed | Lie groups A problem oriented introduction via matrix groups Harriet Pollatsek |
| title_short | Lie groups |
| title_sort | lie groups a problem oriented introduction via matrix groups |
| title_sub | A problem oriented introduction via matrix groups |
| topic | Lie groups Lie groups Problems, exercises, etc Matrix groups Lie-Gruppe (DE-588)4035695-4 gnd Matrizengruppe (DE-588)4169127-1 gnd |
| topic_facet | Lie groups Lie groups Problems, exercises, etc Matrix groups Lie-Gruppe Matrizengruppe Aufgabensammlung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018612202&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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