The geometry of Jordan and Lie structures:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin ; Heidelberg ; New York
Springer
2000
|
| Series: | Lecture notes in mathematics
1754 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XVI, 269 S. |
| ISBN: | 3540414266 |
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| 100 | 1 | |a Bertram, Wolfgang |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a The geometry of Jordan and Lie structures |c Wolfgang Bertram |
| 264 | 1 | |a Berlin ; Heidelberg ; New York |b Springer |c 2000 | |
| 300 | |a XVI, 269 S. | ||
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Record in the Search Index
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| adam_text | Table of Contents
0. Introduction VII
First Part: The Jordan Lie functor
1. Symmetric spaces and the Lie functor 1
1. Lie functor: group theoretic version 2
2. Lie functor: differential geometric version 6
3. Symmetries and group of displacements 10
4. The multiplication map 13
5. Representations of symmetric spaces 15
6. Examples 18
Appendix A: Tangent objects and their extensions 32
Appendix B: Affine Connections 35
II. Prehomogeneous symmetric spaces and Jordan algebras 42
1. Prehomogeneous symmetric spaces 42
2. Quadratic prehomogeneous symmetric spaces 45
3. Examples 54
4. Symmetric submanifolds and Helwig spaces 57
III. The Jordan Lie functor 61
1. Complexifications of symmetric spaces 62
2. Twisted complex symmetric spaces and Hermitian JTS 65
3. Polarizations, graded Lie algebras and Jordan pairs 70
4. Jordan extensions and the geometric Jordan Lie functor 74
IV. The classical spaces 81
1. Examples 82
2. Principles of classification 92
V. Non degenerate spaces 97
1. Pseudo Riemannian symmetric spaces 98
2. Pseudo Hermitian and para Hermitian symmetric spaces 103
3. Pseudo Riemannian symmetric spaces with twist 106
4. Semisimple Jordan algebras 107
5. Compact spaces and duality Ill
Second Part: Conformal group and global theory
VI. Integration of Jordan structures 116
1. Circled spaces 118
2. Ruled spaces 120
3. Integrated version of Jordan triple systems 122
Appendix A: Integrability of almost complex structures 124
VI
VII. The conformal Lie algebra 127
1. Euler operators and conformal Lie algebra 128
2. The Kantor Koecher Tits construction 132
3. General structure of the conformal Lie algebra 138
VIII. Conformal group and conformal completion 143
1. Conformal group: general properties 144
2. Conformal group: fine structure 150
3. The conformal completion and its dual 156
4. Conformal completion of the classical spaces 160
Appendix A: Some identities for Jordan triple systems 166
Appendix B: Equivariant bundles over homogeneous spaces 167
IX. Liouville theorem and fundamental theorem 171
1. Liouville theorem and fundamental theorem 171
2. Application to the classical spaces 177
X. Algebraic structures of symmetric spaces with twist 184
1. Open symmetric orbits in the conformal completion 185
2. Harish Chandra realization 188
3. Jordan analog of the Campbell Hausdorff formula 192
4. The exponential map 200
5. One parameter subspaces and Peirce decomposition 204
6. Non degenerate spaces 208
Appendix A: Power associativity 213
XI. Spaces of the first and of the second kind 216
1. Spaces of the first kind and Jordan algebras 216
2. Cayley transform and tube realizations 220
3. Causal symmetric spaces 226
4. Helwig spaces and the extension problem 230
5. Examples 232
XII. Tables 240
1. Simple Jordan algebras 240
2. Simple Jordan triple systems 243
3. Conformal groups and conformal completions 245
4. Classification of simple symmetric spaces with twist 248
XIII. Further topics 254
Bibliography 256
Notation 263
Index 266
|
| any_adam_object | 1 |
| author | Bertram, Wolfgang |
| author_facet | Bertram, Wolfgang |
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| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
| dewey-raw | 512.24 |
| dewey-search | 512.24 |
| dewey-sort | 3512.24 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
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| indexdate | 2024-07-09T18:46:16Z |
| institution | BVB |
| isbn | 3540414266 |
| language | English |
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| physical | XVI, 269 S. |
| publishDate | 2000 |
| publishDateSearch | 2000 |
| publishDateSort | 2000 |
| publisher | Springer |
| record_format | marc |
| series | Lecture notes in mathematics |
| series2 | Lecture notes in mathematics |
| spelling | Bertram, Wolfgang Verfasser aut The geometry of Jordan and Lie structures Wolfgang Bertram Berlin ; Heidelberg ; New York Springer 2000 XVI, 269 S. txt rdacontent n rdamedia nc rdacarrier Lecture notes in mathematics 1754 Jordan algebras Lie algebras Lie-Algebra (DE-588)4130355-6 gnd rswk-swf Jordan-Algebra (DE-588)4162770-2 gnd rswk-swf Differentialgeometrie (DE-588)4012248-7 gnd rswk-swf Jordan-Algebra (DE-588)4162770-2 s Lie-Algebra (DE-588)4130355-6 s Differentialgeometrie (DE-588)4012248-7 s DE-604 Lecture notes in mathematics 1754 (DE-604)BV000676446 1754 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009187236&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Bertram, Wolfgang The geometry of Jordan and Lie structures Lecture notes in mathematics Jordan algebras Lie algebras Lie-Algebra (DE-588)4130355-6 gnd Jordan-Algebra (DE-588)4162770-2 gnd Differentialgeometrie (DE-588)4012248-7 gnd |
| subject_GND | (DE-588)4130355-6 (DE-588)4162770-2 (DE-588)4012248-7 |
| title | The geometry of Jordan and Lie structures |
| title_auth | The geometry of Jordan and Lie structures |
| title_exact_search | The geometry of Jordan and Lie structures |
| title_full | The geometry of Jordan and Lie structures Wolfgang Bertram |
| title_fullStr | The geometry of Jordan and Lie structures Wolfgang Bertram |
| title_full_unstemmed | The geometry of Jordan and Lie structures Wolfgang Bertram |
| title_short | The geometry of Jordan and Lie structures |
| title_sort | the geometry of jordan and lie structures |
| topic | Jordan algebras Lie algebras Lie-Algebra (DE-588)4130355-6 gnd Jordan-Algebra (DE-588)4162770-2 gnd Differentialgeometrie (DE-588)4012248-7 gnd |
| topic_facet | Jordan algebras Lie algebras Lie-Algebra Jordan-Algebra Differentialgeometrie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009187236&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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