Quadratic mappings and Clifford algebras:
Gespeichert in:
| Beteiligte Personen: | , |
|---|---|
| Format: | Buch |
| Sprache: | Englisch |
| Veröffentlicht: |
Basel [u.a.]
Birkhäuser
2008
|
| Schlagwörter: | |
| Links: | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016280692&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| Umfang: | XIII, 504 S. |
| ISBN: | 3764386053 9783764386054 |
Internformat
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| 100 | 1 | |a Helmstetter, Jacques |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Quadratic mappings and Clifford algebras |c Jacques Helmstetter ; Artibano Micali |
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Datensatz im Suchindex
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|---|---|
| adam_text | JACQUES HELMSTETTER ARTIBANO MICALI QUADRATIC MAPPINGS AND CLIFFORD
ALGEBRAS BIRKHAUSER BASEL * BOSTON * BERLIN INTRODUCTION IX 1 ALGEBRAIC
PRELIMINARIES 1.1 SOME GENERAL NOTATION AND DEFINITIONS 1 1.2 UNIVERSAL
OBJECTS IN A CATEGORY 2 1.3 EXAMPLES OF UNIVERSAL OBJECTS 4 1.4 TENSOR
ALGEBRAS AND SYMMETRIC ALGEBRAS 8 1.5 FUNCTORS 10 1.6 EXACT SEQUENCES 12
1.7 PROJECTIVE MODULES AND FLAT MODULES 14 1.8 FINITELY PRESENTED
MODULES 15 1.9 CHANGES OF BASIC RINGS 17 1.10 RINGS AND MODULES OF
FRACTIONS 21 1.11 LOCALIZATION AND GLOBALIZATION 25 1.12 FINITELY
GENERATED MODULES 30 1.13 SOME APPLICATIONS 37 EXERCISES 42 2 QUADRATIC
MAPPINGS 2.1 GENERALITIES 53 2.2 CHANGES OF BASIC RING AND LOCALIZATIONS
57 2.3 NONDEGENERATE QUADRATIC MAPPINGS 59 2.4 OPERATIONS ON QUADRATIC
MAPPINGS AND SYMMETRIC BILINEAR MAPPINGS 63 2.5 HYPERBOLIC AND METABOLIC
SPACES 67 2.6 ORTHOGONAL DECOMPOSITIONS OF QUADRATIC SPACES 72 2.7 WITT
RINGS 78 2.8 EXAMPLES OF WITT RINGS 83 EXERCISES 93 VI CONTENTS 3
CLIFFORD ALGEBRAS 3.1 DEFINITIONS AND ELEMENTARY PROPERTIES 105 3.2 THE
PARITY GRADING OF CLIFFORD ALGEBRAS 112 3.3 CLIFFORD ALGEBRAS OF FREE
MODULES OF RANK 2 117 3.4 GRADED QUADRATIC EXTENSIONS 122 3.5 GRADED
AZUMAYA ALGEBRAS 131 3.6 TRACES AND DETERMINANTS 144 3.7 CLIFFORD
ALGEBRAS OF QUADRATIC SPACES 149 3.8 DISCRIMINANT MODULES, QUADRATIC
EXTENSIONS AND QUATERNION ALGEBRAS 154 EXERCISES 164 4
COMULTIPLICATIONS. EXPONENTIALS. DEFORMATIONS 4.1 COALGEBRAS AND
COMODULES 175 4.2 ALGEBRAS AND COALGEBRAS GRADED BY PARITIES 181 4.3
EXTERIOR ALGEBRAS 185 4.4 INTERIOR PRODUCTS IN CLIFFORD ALGEBRAS 190 4.5
EXPONENTIALS IN EVEN EXTERIOR SUBALGEBRAS 195 4.6 SYSTEMS OF DIVIDED
POWERS 199 4.7 DEFORMATIONS OF CLIFFORD ALGEBRAS 201 4.8 APPLICATIONS OF
DEFORMATIONS 210 EXERCISES 219 5 ORTHOGONAL GROUPS AND LIPSCHITZ GROUPS
5.1 TWISTED INNER AUTOMORPHISMS AND ORTHOGONAL GROUPS 232 5.2
FILTRATIONS OF CLIFFORD ALGEBRAS 243 5.3 LIPSCHITZ MONOIDS AND DERIVED
GROUPS 249 5.4 THE INVARIANCE PROPERTY 258 5.5 ASSOCIATED LIE ALGEBRAS
261 5.6 FIRST RESULTS ABOUT ORTHOGONAL TRANSFORMATIONS 267 5.7 PRODUCTS
OF REFLECTIONS WHEN K IS A LOCAL RING 272 5.8 FURTHER RESULTS ABOUT
ORTHOGONAL TRANSFORMATIONS 281 5.9 MORE INFORMATION ABOUT EXTERIOR
ALGEBRAS 287 5.10 THE LIPSCHITZ MONOID LIP(M) WHEN K IS A FIELD 296
EXERCISES 303 6 FURTHER ALGEBRAIC DEVELOPMENTS 6.1 MODULES OVER A
NONCOMMUTATIVE ALGEBRA 323 6.2 GRADED MODULES OVER A GRADED ALGEBRA 327
6.3 GRADED SEMI-SIMPLE MODULES 334 6.4 GRADED MORITA THEORY 337 6.5
GRADED SEPARABLE ALGEBRAS 344 CONTENTS VII 6.6 GRADED CENTRAL SIMPLE
ALGEBRAS OVER A FIELD 353 6.7 MORE INFORMATION ABOUT GRADED AZUMAYA
ALGEBRAS 358 6.8 INVOLUTIONS ON GRADED CENTRAL SIMPLE ALGEBRAS 365
EXERCISES 376 7 HYPERBOLIC SPACES 7.1 SOME REPRESENTATIONS OF CLIFFORD
ALGEBRAS 391 7.2 THE CARTAN-CHEVALLEY MAPPING 395 7.3 THE BIJECTION
C(V) / MAX (U) C(V) - C(M) 403 7.4 THE CARTAN-CHEVALLEY
CRITERION 409 7.5 APPLICATIONS TO LIPSCHITZ MONOIDS 414 7.6 APPLICATIONS
TO TOTALLY ISOTROPIC DIRECT SUMMANDS OF MAXIMAL RANK 421 EXERCISES 425 8
COMPLEMENTS ABOUT WITT RINGS AND OTHER TOPICS 8.1 WITT RINGS OVER LOCAL
RINGS WHEN 2 IS INVERTIBLE 439 8.2 CONTINUATION WHEN 2 IS NOT INVERTIBLE
445 8.3 WITT RINGS OF PRIIFER RINGS 453 8.4 QUADRATIC FORMS IN
CHARACTERISTIC 2 461 8.5 CLIFFORD ALGEBRAS IN CHARACTERISTIC 2 464 8.6
THE GROUP OF CLASSES OF CLIFFORD ALGEBRAS 468 EXERCISES 478 BIBLIOGRAPHY
BOOKS AND BOOKLETS 489 OTHER PUBLICATIONS 492 INDEX OF DEFINITIONS 499
INDEX OF NOTATION 503
|
| any_adam_object | 1 |
| author | Helmstetter, Jacques Micali, Artibano |
| author_facet | Helmstetter, Jacques Micali, Artibano |
| author_role | aut aut |
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| author_variant | j h jh a m am |
| building | Verbundindex |
| bvnumber | BV023077622 |
| callnumber-first | Q - Science |
| callnumber-label | QA199 |
| callnumber-raw | QA199 |
| callnumber-search | QA199 |
| callnumber-sort | QA 3199 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 180 SK 230 |
| ctrlnum | (OCoLC)175285188 (DE-599)DNB985454423 |
| dewey-full | 512.57 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
| dewey-raw | 512.57 |
| dewey-search | 512.57 |
| dewey-sort | 3512.57 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV023077622 |
| illustrated | Not Illustrated |
| indexdate | 2024-12-20T13:08:06Z |
| institution | BVB |
| isbn | 3764386053 9783764386054 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-016280692 |
| oclc_num | 175285188 |
| open_access_boolean | |
| owner | DE-29 DE-703 DE-11 DE-824 |
| owner_facet | DE-29 DE-703 DE-11 DE-824 |
| physical | XIII, 504 S. |
| publishDate | 2008 |
| publishDateSearch | 2008 |
| publishDateSort | 2008 |
| publisher | Birkhäuser |
| record_format | marc |
| spellingShingle | Helmstetter, Jacques Micali, Artibano Quadratic mappings and Clifford algebras Clifford algebras Forms, Quadratic Quadratischer Modul (DE-588)4819733-6 gnd Clifford-Algebra (DE-588)4199958-7 gnd Quadratische Form (DE-588)4128297-8 gnd |
| subject_GND | (DE-588)4819733-6 (DE-588)4199958-7 (DE-588)4128297-8 |
| title | Quadratic mappings and Clifford algebras |
| title_auth | Quadratic mappings and Clifford algebras |
| title_exact_search | Quadratic mappings and Clifford algebras |
| title_full | Quadratic mappings and Clifford algebras Jacques Helmstetter ; Artibano Micali |
| title_fullStr | Quadratic mappings and Clifford algebras Jacques Helmstetter ; Artibano Micali |
| title_full_unstemmed | Quadratic mappings and Clifford algebras Jacques Helmstetter ; Artibano Micali |
| title_short | Quadratic mappings and Clifford algebras |
| title_sort | quadratic mappings and clifford algebras |
| topic | Clifford algebras Forms, Quadratic Quadratischer Modul (DE-588)4819733-6 gnd Clifford-Algebra (DE-588)4199958-7 gnd Quadratische Form (DE-588)4128297-8 gnd |
| topic_facet | Clifford algebras Forms, Quadratic Quadratischer Modul Clifford-Algebra Quadratische Form |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016280692&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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