Differential geometry, Lie groups, and symmetric spaces over general base fields and rings:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Providence, RI
American Mathematical Society
2008
|
| Schriftenreihe: | Memoirs of the American Mathematical Society
900 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Angabe in der Vorlage: Volume 192, number 900 (end of volume) Includes bibliographical references |
| Beschreibung: | IX, 202 S. |
| ISBN: | 9780821840917 |
Internformat
MARC
| LEADER | 00000nam a2200000 cb4500 | ||
|---|---|---|---|
| 001 | BV023214529 | ||
| 003 | DE-604 | ||
| 005 | 20150323 | ||
| 007 | t | ||
| 008 | 080314s2008 xxu |||| 00||| eng d | ||
| 010 | |a 2007060585 | ||
| 020 | |a 9780821840917 |9 978-0-8218-4091-7 | ||
| 035 | |a (OCoLC)263722947 | ||
| 035 | |a (DE-599)BVBBV023214529 | ||
| 040 | |a DE-604 |b ger |e rakwb | ||
| 041 | 0 | |a eng | |
| 044 | |a xxu |c US | ||
| 049 | |a DE-355 |a DE-29T |a DE-11 |a DE-188 |a DE-384 |a DE-83 | ||
| 050 | 0 | |a QA252.3 | |
| 082 | 0 | |a 512/.482 |2 22 | |
| 082 | 0 | |a 510 |2 22 | |
| 082 | 0 | |a 510 s | |
| 100 | 1 | |a Bertram, Wolfgang |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Differential geometry, Lie groups, and symmetric spaces over general base fields and rings |c Wolfgang Bertram |
| 264 | 1 | |a Providence, RI |b American Mathematical Society |c 2008 | |
| 300 | |a IX, 202 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Memoirs of the American Mathematical Society |v 900 | |
| 500 | |a Angabe in der Vorlage: Volume 192, number 900 (end of volume) | ||
| 500 | |a Includes bibliographical references | ||
| 650 | 4 | |a Infinite dimensional Lie algebras | |
| 650 | 4 | |a Infinite-dimensional manifolds | |
| 650 | 4 | |a Symmetric spaces | |
| 650 | 4 | |a Geometry, Differential | |
| 650 | 0 | 7 | |a Differentialgeometrie |0 (DE-588)4012248-7 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Symmetrischer Raum |0 (DE-588)4184206-6 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Unendlichdimensionale Lie-Algebra |0 (DE-588)4434344-9 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Unendlichdimensionale Lie-Algebra |0 (DE-588)4434344-9 |D s |
| 689 | 0 | 1 | |a Differentialgeometrie |0 (DE-588)4012248-7 |D s |
| 689 | 0 | 2 | |a Symmetrischer Raum |0 (DE-588)4184206-6 |D s |
| 689 | 0 | |5 DE-604 | |
| 830 | 0 | |a Memoirs of the American Mathematical Society |v 900 |w (DE-604)BV008000141 |9 900 | |
| 856 | 4 | 2 | |m HBZ Datenaustausch |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016400552&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-016400552 | ||
Datensatz im Suchindex
| _version_ | 1804137498278887424 |
|---|---|
| adam_text | Contents
Introduction 1
I. Basic notions
1. Differential calculus 14
2. Manifolds 20
3. Tangent bundle and general fiber bundles 22
4. The Lie bracket of vector fields 25
5. Lie groups and symmetric spaces: basic facts 30
II. Interpretation of tangent objects via scalar extensions
6. Scalar extensions. I: Tangent functor and dual numbers 36
7. Scalar extensions. II: Higher order tangent functors 42
8. Scalar extensions. Ill: Jet functor and truncated polynomial rings 50
III. Second order differential geometry
9. The structure of the tangent bundle of a vector bundle 57
10. Linear connections. I: Linear structures on bilinear bundles 61
11. Linear connections. II: Sprays 08
12. Linear connections. Ill: Covariant derivative 71
13. Natural operations. I: Exterior derivative of a one-form 73
14. Natural operations. II: The Lie bracket revisited 75
IV. Third and higher order differential geometry
15. The structure of TkF: Multilinear bundles 79
16. The structure of TkF: Multilinear connections 83
17. Construction of multilinear connections 87
18. Curvature 91
19. Linear structures on jet bundles 95
v
vi TABLE OF CONTENTS
20. Shifts and symmetrization 98
21. Remarks on differential operators and symbols 102
22. The exterior derivative 106
V. Lie Theory
23. The three canonical connections of a Lie group 110
24. The structure of higher order tangent groups 116
25. Exponential map and Campbell-Hausdorff formula 124
26. The canonical connection of a symmetric space 128
27. The higher order tangent structure of symmetric spaces 134
VI.Diffeomorphism Groups and the exponential jet
28. Group structure on the space of sections of TkM 139
29. The exponential jet for vector fields 144
30. The exponential jet of a symmetric space 148
31. Remarks on the exponential jet of a general connection 151
32. Prom germs to jets and from jets to germs 153
Appendix L. Limitations 156
Appendix G. Generalizations 159
Appendix: Multilinear Geometry
BA. Bilinear algebra 161
MA. Multilinear algebra 168
SA. Symmetric and shift invariant multilinear algebra 182
PG. Polynomial groups 192
References 199
|
| adam_txt |
Contents
Introduction 1
I. Basic notions
1. Differential calculus 14
2. Manifolds 20
3. Tangent bundle and general fiber bundles 22
4. The Lie bracket of vector fields 25
5. Lie groups and symmetric spaces: basic facts 30
II. Interpretation of tangent objects via scalar extensions
6. Scalar extensions. I: Tangent functor and dual numbers 36
7. Scalar extensions. II: Higher order tangent functors 42
8. Scalar extensions. Ill: Jet functor and truncated polynomial rings 50
III. Second order differential geometry
9. The structure of the tangent bundle of a vector bundle 57
10. Linear connections. I: Linear structures on bilinear bundles 61
11. Linear connections. II: Sprays 08
12. Linear connections. Ill: Covariant derivative 71
13. Natural operations. I: Exterior derivative of a one-form 73
14. Natural operations. II: The Lie bracket revisited 75
IV. Third and higher order differential geometry
15. The structure of TkF: Multilinear bundles 79
16. The structure of TkF: Multilinear connections 83
17. Construction of multilinear connections 87
18. Curvature 91
19. Linear structures on jet bundles 95
v
vi TABLE OF CONTENTS
20. Shifts and symmetrization 98
21. Remarks on differential operators and symbols 102
22. The exterior derivative 106
V. Lie Theory
23. The three canonical connections of a Lie group 110
24. The structure of higher order tangent groups 116
25. Exponential map and Campbell-Hausdorff formula 124
26. The canonical connection of a symmetric space 128
27. The higher order tangent structure of symmetric spaces 134
VI.Diffeomorphism Groups and the exponential jet
28. Group structure on the space of sections of TkM 139
29. The exponential jet for vector fields 144
30. The exponential jet of a symmetric space 148
31. Remarks on the exponential jet of a general connection 151
32. Prom germs to jets and from jets to germs 153
Appendix L. Limitations 156
Appendix G. Generalizations 159
Appendix: Multilinear Geometry
BA. Bilinear algebra 161
MA. Multilinear algebra 168
SA. Symmetric and shift invariant multilinear algebra 182
PG. Polynomial groups 192
References 199 |
| any_adam_object | 1 |
| any_adam_object_boolean | 1 |
| author | Bertram, Wolfgang |
| author_facet | Bertram, Wolfgang |
| author_role | aut |
| author_sort | Bertram, Wolfgang |
| author_variant | w b wb |
| building | Verbundindex |
| bvnumber | BV023214529 |
| callnumber-first | Q - Science |
| callnumber-label | QA252 |
| callnumber-raw | QA252.3 |
| callnumber-search | QA252.3 |
| callnumber-sort | QA 3252.3 |
| callnumber-subject | QA - Mathematics |
| ctrlnum | (OCoLC)263722947 (DE-599)BVBBV023214529 |
| dewey-full | 512/.482 510 510S |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra 510 - Mathematics |
| dewey-raw | 512/.482 510 510 s |
| dewey-search | 512/.482 510 510 s |
| dewey-sort | 3512 3482 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| discipline_str_mv | Mathematik |
| format | Book |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>02105nam a2200517 cb4500</leader><controlfield tag="001">BV023214529</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">20150323 </controlfield><controlfield tag="007">t</controlfield><controlfield tag="008">080314s2008 xxu |||| 00||| eng d</controlfield><datafield tag="010" ind1=" " ind2=" "><subfield code="a">2007060585</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9780821840917</subfield><subfield code="9">978-0-8218-4091-7</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)263722947</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV023214529</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield><subfield code="e">rakwb</subfield></datafield><datafield tag="041" ind1="0" ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="044" ind1=" " ind2=" "><subfield code="a">xxu</subfield><subfield code="c">US</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-355</subfield><subfield code="a">DE-29T</subfield><subfield code="a">DE-11</subfield><subfield code="a">DE-188</subfield><subfield code="a">DE-384</subfield><subfield code="a">DE-83</subfield></datafield><datafield tag="050" ind1=" " ind2="0"><subfield code="a">QA252.3</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">512/.482</subfield><subfield code="2">22</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">510</subfield><subfield code="2">22</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">510 s</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Bertram, Wolfgang</subfield><subfield code="e">Verfasser</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Differential geometry, Lie groups, and symmetric spaces over general base fields and rings</subfield><subfield code="c">Wolfgang Bertram</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Providence, RI</subfield><subfield code="b">American Mathematical Society</subfield><subfield code="c">2008</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">IX, 202 S.</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="b">n</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="b">nc</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="490" ind1="1" ind2=" "><subfield code="a">Memoirs of the American Mathematical Society</subfield><subfield code="v">900</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">Angabe in der Vorlage: Volume 192, number 900 (end of volume)</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">Includes bibliographical references</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Infinite dimensional Lie algebras</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Infinite-dimensional manifolds</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Symmetric spaces</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Geometry, Differential</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Differentialgeometrie</subfield><subfield code="0">(DE-588)4012248-7</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Symmetrischer Raum</subfield><subfield code="0">(DE-588)4184206-6</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Unendlichdimensionale Lie-Algebra</subfield><subfield code="0">(DE-588)4434344-9</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="689" ind1="0" ind2="0"><subfield code="a">Unendlichdimensionale Lie-Algebra</subfield><subfield code="0">(DE-588)4434344-9</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2="1"><subfield code="a">Differentialgeometrie</subfield><subfield code="0">(DE-588)4012248-7</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2="2"><subfield code="a">Symmetrischer Raum</subfield><subfield code="0">(DE-588)4184206-6</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2=" "><subfield code="5">DE-604</subfield></datafield><datafield tag="830" ind1=" " ind2="0"><subfield code="a">Memoirs of the American Mathematical Society</subfield><subfield code="v">900</subfield><subfield code="w">(DE-604)BV008000141</subfield><subfield code="9">900</subfield></datafield><datafield tag="856" ind1="4" ind2="2"><subfield code="m">HBZ Datenaustausch</subfield><subfield code="q">application/pdf</subfield><subfield code="u">http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016400552&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA</subfield><subfield code="3">Inhaltsverzeichnis</subfield></datafield><datafield tag="999" ind1=" " ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-016400552</subfield></datafield></record></collection> |
| id | DE-604.BV023214529 |
| illustrated | Not Illustrated |
| index_date | 2024-07-02T20:13:27Z |
| indexdate | 2024-07-09T21:13:15Z |
| institution | BVB |
| isbn | 9780821840917 |
| language | English |
| lccn | 2007060585 |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-016400552 |
| oclc_num | 263722947 |
| open_access_boolean | |
| owner | DE-355 DE-BY-UBR DE-29T DE-11 DE-188 DE-384 DE-83 |
| owner_facet | DE-355 DE-BY-UBR DE-29T DE-11 DE-188 DE-384 DE-83 |
| physical | IX, 202 S. |
| publishDate | 2008 |
| publishDateSearch | 2008 |
| publishDateSort | 2008 |
| publisher | American Mathematical Society |
| record_format | marc |
| series | Memoirs of the American Mathematical Society |
| series2 | Memoirs of the American Mathematical Society |
| spelling | Bertram, Wolfgang Verfasser aut Differential geometry, Lie groups, and symmetric spaces over general base fields and rings Wolfgang Bertram Providence, RI American Mathematical Society 2008 IX, 202 S. txt rdacontent n rdamedia nc rdacarrier Memoirs of the American Mathematical Society 900 Angabe in der Vorlage: Volume 192, number 900 (end of volume) Includes bibliographical references Infinite dimensional Lie algebras Infinite-dimensional manifolds Symmetric spaces Geometry, Differential Differentialgeometrie (DE-588)4012248-7 gnd rswk-swf Symmetrischer Raum (DE-588)4184206-6 gnd rswk-swf Unendlichdimensionale Lie-Algebra (DE-588)4434344-9 gnd rswk-swf Unendlichdimensionale Lie-Algebra (DE-588)4434344-9 s Differentialgeometrie (DE-588)4012248-7 s Symmetrischer Raum (DE-588)4184206-6 s DE-604 Memoirs of the American Mathematical Society 900 (DE-604)BV008000141 900 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016400552&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Bertram, Wolfgang Differential geometry, Lie groups, and symmetric spaces over general base fields and rings Memoirs of the American Mathematical Society Infinite dimensional Lie algebras Infinite-dimensional manifolds Symmetric spaces Geometry, Differential Differentialgeometrie (DE-588)4012248-7 gnd Symmetrischer Raum (DE-588)4184206-6 gnd Unendlichdimensionale Lie-Algebra (DE-588)4434344-9 gnd |
| subject_GND | (DE-588)4012248-7 (DE-588)4184206-6 (DE-588)4434344-9 |
| title | Differential geometry, Lie groups, and symmetric spaces over general base fields and rings |
| title_auth | Differential geometry, Lie groups, and symmetric spaces over general base fields and rings |
| title_exact_search | Differential geometry, Lie groups, and symmetric spaces over general base fields and rings |
| title_exact_search_txtP | Differential geometry, Lie groups, and symmetric spaces over general base fields and rings |
| title_full | Differential geometry, Lie groups, and symmetric spaces over general base fields and rings Wolfgang Bertram |
| title_fullStr | Differential geometry, Lie groups, and symmetric spaces over general base fields and rings Wolfgang Bertram |
| title_full_unstemmed | Differential geometry, Lie groups, and symmetric spaces over general base fields and rings Wolfgang Bertram |
| title_short | Differential geometry, Lie groups, and symmetric spaces over general base fields and rings |
| title_sort | differential geometry lie groups and symmetric spaces over general base fields and rings |
| topic | Infinite dimensional Lie algebras Infinite-dimensional manifolds Symmetric spaces Geometry, Differential Differentialgeometrie (DE-588)4012248-7 gnd Symmetrischer Raum (DE-588)4184206-6 gnd Unendlichdimensionale Lie-Algebra (DE-588)4434344-9 gnd |
| topic_facet | Infinite dimensional Lie algebras Infinite-dimensional manifolds Symmetric spaces Geometry, Differential Differentialgeometrie Symmetrischer Raum Unendlichdimensionale Lie-Algebra |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016400552&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV008000141 |
| work_keys_str_mv | AT bertramwolfgang differentialgeometryliegroupsandsymmetricspacesovergeneralbasefieldsandrings |