The Minnesota notes on Jordan algebras and their applications:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | German |
| Published: |
Berlin u.a.
Springer
1999
|
| Series: | Lecture notes in mathematics
1710 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | IX, 173 S. |
| ISBN: | 3540663606 |
Staff View
MARC
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Record in the Search Index
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|---|---|
| adam_text | Contents
Chapter I. Domains of Positivity 1
§1. Some notions and notations 1
§2. The notion of a domain of positivity 5
§3. The automorphisms of a domain of positivity 9
§4. Norms of a domain of positivity 12
§5. Examples 14
§6. Differential operators 17
§7. An invariant line element 21
§8. The map y ( »• y* 23
§9. Homogeneous domains of positivity 29
Notes 32
Editors Notes 32
Chapter II. Omega Domains 35
§1. The notion of an w domain 35
§2. Some examples 38
§3. The geodesies of an w domain 40
§4. Non associative algebras 45
§5. w domains and Jordan algebras 48
Notes 50
Editors Notes 51
VIII Contents
Chapter III. Jordan Algebras 53
§1. Jordan algebras 53
§2. The radical of a Jordan algebra 58
§3. The unit element of a Jordan algebra 61
§4. The decomposition theorem 64
§5. The inverse 66
§6. Constructions of Jordan algebras 68
Notes 71
Editors Notes 71
Chapter IV. Real and Complex Jordan Algebras 73
§1. The quadratic representation 73
§2. Mutations 76
§3. A generalization of the fundamental formula 78
§4. The exponential 82
§5. The associated Lie algebra 85
§6. Direct sums 89
Notes 90
Editors Notes 91
Chapter V. Complex Jordan Algebras 93
§ 1. Minimal polynomial and eigenvalues 93
§2. Minimal relations 95
§3. The minimal decomposition 97
§4. Applications of the minimal decomposition 99
§5. The eigenvalues of L{u) and P(u) 102
§6. The embedding of real Jordan algebras 105
Notes 107
Editors Notes 108
Contents IX
Chapter VI. Jordan Algebras and Omega Domains 109
§1. The w domain of a Jordan algebra 109
§2. The Jordan algebra of an w domain 113
§3. Jordan algebras with equivalent w domains 115
§4. Formally real Jordan algebras 117
§5. Homogeneous domains of positivity 119
§6. Elementary functions on formally real Jordan algebras 122
§7. Direct sums 124
Notes 125
Editors notes 126
Chapter VII. Half Spaces 127
§1. The half space of a semisimple Jordan algebra 127
§2. The isotropy group Ho 131
§3. Application to the set if 135
§4. Biholomorphic automorphisms of half spaces 140
§5. Formally real Jordan algebras 142
§6. The bounded symmetric domain Z 145
§7. Remarks on classification 147
§8. One typical example 148
Notes 153
Editors Notes 153
Appendix: The Bergman kernel function 157
§1. Reproducing kernels 157
§2. Domains in complex number space 159
Notes 161
Editors Notes 161
Bibliography 163
Index 171
Biography 175
|
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| illustrated | Not Illustrated |
| indexdate | 2024-07-09T18:32:25Z |
| institution | BVB |
| isbn | 3540663606 |
| language | German |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-008644182 |
| oclc_num | 440218870 |
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| physical | IX, 173 S. |
| publishDate | 1999 |
| publishDateSearch | 1999 |
| publishDateSort | 1999 |
| publisher | Springer |
| record_format | marc |
| series | Lecture notes in mathematics |
| series2 | Lecture notes in mathematics |
| spelling | Koecher, Max 1924-1990 Verfasser (DE-588)117714291 aut The Minnesota notes on Jordan algebras and their applications Max Koecher Berlin u.a. Springer 1999 IX, 173 S. txt rdacontent n rdamedia nc rdacarrier Lecture notes in mathematics 1710 Jordan-Algebra (DE-588)4162770-2 gnd rswk-swf Jordan-Algebra (DE-588)4162770-2 s DE-604 Lecture notes in mathematics 1710 (DE-604)BV000676446 1710 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008644182&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Koecher, Max 1924-1990 The Minnesota notes on Jordan algebras and their applications Lecture notes in mathematics Jordan-Algebra (DE-588)4162770-2 gnd |
| subject_GND | (DE-588)4162770-2 |
| title | The Minnesota notes on Jordan algebras and their applications |
| title_auth | The Minnesota notes on Jordan algebras and their applications |
| title_exact_search | The Minnesota notes on Jordan algebras and their applications |
| title_full | The Minnesota notes on Jordan algebras and their applications Max Koecher |
| title_fullStr | The Minnesota notes on Jordan algebras and their applications Max Koecher |
| title_full_unstemmed | The Minnesota notes on Jordan algebras and their applications Max Koecher |
| title_short | The Minnesota notes on Jordan algebras and their applications |
| title_sort | the minnesota notes on jordan algebras and their applications |
| topic | Jordan-Algebra (DE-588)4162770-2 gnd |
| topic_facet | Jordan-Algebra |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008644182&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000676446 |
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