Clifford algebras and the classical groups:
The Clifford algebras of real quadratic forms and their complexifications are studied here in detail, and those parts which are immediately relevant to theoretical physics are seen in the proper broad context. Central to the work is the classification of the conjugation and reversion anti-involution...
Saved in:
| Main Author: | |
|---|---|
| Format: | Electronic eBook |
| Language: | English |
| Published: |
Cambridge
Cambridge University Press
1995
|
| Series: | Cambridge studies in advanced mathematics
50 |
| Subjects: | |
| Online Access: | BSB01 FHN01 UBR01 Volltext |
| Summary: | The Clifford algebras of real quadratic forms and their complexifications are studied here in detail, and those parts which are immediately relevant to theoretical physics are seen in the proper broad context. Central to the work is the classification of the conjugation and reversion anti-involutions that arise naturally in the theory. It is of interest that all the classical groups play essential roles in this classification. Other features include detailed sections on conformal groups, the eight-dimensional non-associative Cayley algebra, its automorphism group, the exceptional Lie group G2, and the triality automorphism of Spin 8. The book is designed to be suitable for the last year of an undergraduate course or the first year of a postgraduate course |
| Physical Description: | 1 online resource (x, 295 Seiten) |
| ISBN: | 9780511470912 |
| DOI: | 10.1017/CBO9780511470912 |
Staff View
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| 505 | 8 | |a 1. Linear spaces -- 2. Real and complex algebras -- 3. Exact sequences -- 4. Real quadratic spaces -- 5. The classification of real quadratic spaces -- 6. Anti-involutions of R(n) -- 7. Anti-involutions of C(n) -- 8. Quaternions -- 9. Quaternionic linear spaces -- 10. Anti-involutions of H(n) -- 11. Tensor products of algebras -- 12. Anti-involutions of [superscript 2]K(n) -- 13. The classical groups -- 14. Quadric Grassmannians -- 15. Clifford algebras -- 16. Spin groups -- 17. Conjugation -- 18. 2 x 2 Clifford matrices -- 19. The Cayley algebra -- 20. Topological spaces -- 21. Manifolds -- 22. Lie groups -- 23. Conformal groups -- 24. Triality | |
| 520 | |a The Clifford algebras of real quadratic forms and their complexifications are studied here in detail, and those parts which are immediately relevant to theoretical physics are seen in the proper broad context. Central to the work is the classification of the conjugation and reversion anti-involutions that arise naturally in the theory. It is of interest that all the classical groups play essential roles in this classification. Other features include detailed sections on conformal groups, the eight-dimensional non-associative Cayley algebra, its automorphism group, the exceptional Lie group G2, and the triality automorphism of Spin 8. The book is designed to be suitable for the last year of an undergraduate course or the first year of a postgraduate course | ||
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Record in the Search Index
| _version_ | 1804176884550860800 |
|---|---|
| any_adam_object | |
| author | Porteous, Ian R. 1930-2011 |
| author_GND | (DE-588)139752633 |
| author_facet | Porteous, Ian R. 1930-2011 |
| author_role | aut |
| author_sort | Porteous, Ian R. 1930-2011 |
| author_variant | i r p ir irp |
| building | Verbundindex |
| bvnumber | BV043942102 |
| classification_rvk | SK 340 SK 230 |
| collection | ZDB-20-CBO |
| contents | 1. Linear spaces -- 2. Real and complex algebras -- 3. Exact sequences -- 4. Real quadratic spaces -- 5. The classification of real quadratic spaces -- 6. Anti-involutions of R(n) -- 7. Anti-involutions of C(n) -- 8. Quaternions -- 9. Quaternionic linear spaces -- 10. Anti-involutions of H(n) -- 11. Tensor products of algebras -- 12. Anti-involutions of [superscript 2]K(n) -- 13. The classical groups -- 14. Quadric Grassmannians -- 15. Clifford algebras -- 16. Spin groups -- 17. Conjugation -- 18. 2 x 2 Clifford matrices -- 19. The Cayley algebra -- 20. Topological spaces -- 21. Manifolds -- 22. Lie groups -- 23. Conformal groups -- 24. Triality |
| ctrlnum | (ZDB-20-CBO)CR9780511470912 (OCoLC)849903110 (DE-599)BVBBV043942102 |
| 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 257 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1017/CBO9780511470912 |
| format | Electronic eBook |
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| id | DE-604.BV043942102 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T07:39:17Z |
| institution | BVB |
| isbn | 9780511470912 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-029351072 |
| oclc_num | 849903110 |
| open_access_boolean | |
| owner | DE-12 DE-92 DE-355 DE-BY-UBR |
| owner_facet | DE-12 DE-92 DE-355 DE-BY-UBR |
| physical | 1 online resource (x, 295 Seiten) |
| psigel | ZDB-20-CBO ZDB-20-CBO BSB_PDA_CBO ZDB-20-CBO FHN_PDA_CBO ZDB-20-CBO UBR Einzelkauf (Lückenergänzung CUP Serien 2018) |
| publishDate | 1995 |
| publishDateSearch | 1995 |
| publishDateSort | 1995 |
| publisher | Cambridge University Press |
| record_format | marc |
| series2 | Cambridge studies in advanced mathematics |
| spelling | Porteous, Ian R. 1930-2011 Verfasser (DE-588)139752633 aut Clifford algebras and the classical groups Ian R. Porteous Clifford Algebras & the Classical Groups Cambridge Cambridge University Press 1995 1 online resource (x, 295 Seiten) txt rdacontent c rdamedia cr rdacarrier Cambridge studies in advanced mathematics 50 1. Linear spaces -- 2. Real and complex algebras -- 3. Exact sequences -- 4. Real quadratic spaces -- 5. The classification of real quadratic spaces -- 6. Anti-involutions of R(n) -- 7. Anti-involutions of C(n) -- 8. Quaternions -- 9. Quaternionic linear spaces -- 10. Anti-involutions of H(n) -- 11. Tensor products of algebras -- 12. Anti-involutions of [superscript 2]K(n) -- 13. The classical groups -- 14. Quadric Grassmannians -- 15. Clifford algebras -- 16. Spin groups -- 17. Conjugation -- 18. 2 x 2 Clifford matrices -- 19. The Cayley algebra -- 20. Topological spaces -- 21. Manifolds -- 22. Lie groups -- 23. Conformal groups -- 24. Triality The Clifford algebras of real quadratic forms and their complexifications are studied here in detail, and those parts which are immediately relevant to theoretical physics are seen in the proper broad context. Central to the work is the classification of the conjugation and reversion anti-involutions that arise naturally in the theory. It is of interest that all the classical groups play essential roles in this classification. Other features include detailed sections on conformal groups, the eight-dimensional non-associative Cayley algebra, its automorphism group, the exceptional Lie group G2, and the triality automorphism of Spin 8. The book is designed to be suitable for the last year of an undergraduate course or the first year of a postgraduate course Clifford algebras Group theory Gruppentheorie (DE-588)4072157-7 gnd rswk-swf Topologische Geometrie (DE-588)4330788-7 gnd rswk-swf Clifford-Algebra (DE-588)4199958-7 gnd rswk-swf Lie-Gruppe (DE-588)4035695-4 gnd rswk-swf Clifford-Algebra (DE-588)4199958-7 s Gruppentheorie (DE-588)4072157-7 s DE-604 Lie-Gruppe (DE-588)4035695-4 s Topologische Geometrie (DE-588)4330788-7 s 1\p DE-604 Erscheint auch als Druck-Ausgabe 978-0-521-55177-9 Erscheint auch als Druck-Ausgabe 978-0-521-11802-6 https://doi.org/10.1017/CBO9780511470912 Verlag URL des Erstveröffentlichers Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Porteous, Ian R. 1930-2011 Clifford algebras and the classical groups 1. Linear spaces -- 2. Real and complex algebras -- 3. Exact sequences -- 4. Real quadratic spaces -- 5. The classification of real quadratic spaces -- 6. Anti-involutions of R(n) -- 7. Anti-involutions of C(n) -- 8. Quaternions -- 9. Quaternionic linear spaces -- 10. Anti-involutions of H(n) -- 11. Tensor products of algebras -- 12. Anti-involutions of [superscript 2]K(n) -- 13. The classical groups -- 14. Quadric Grassmannians -- 15. Clifford algebras -- 16. Spin groups -- 17. Conjugation -- 18. 2 x 2 Clifford matrices -- 19. The Cayley algebra -- 20. Topological spaces -- 21. Manifolds -- 22. Lie groups -- 23. Conformal groups -- 24. Triality Clifford algebras Group theory Gruppentheorie (DE-588)4072157-7 gnd Topologische Geometrie (DE-588)4330788-7 gnd Clifford-Algebra (DE-588)4199958-7 gnd Lie-Gruppe (DE-588)4035695-4 gnd |
| subject_GND | (DE-588)4072157-7 (DE-588)4330788-7 (DE-588)4199958-7 (DE-588)4035695-4 |
| title | Clifford algebras and the classical groups |
| title_alt | Clifford Algebras & the Classical Groups |
| title_auth | Clifford algebras and the classical groups |
| title_exact_search | Clifford algebras and the classical groups |
| title_full | Clifford algebras and the classical groups Ian R. Porteous |
| title_fullStr | Clifford algebras and the classical groups Ian R. Porteous |
| title_full_unstemmed | Clifford algebras and the classical groups Ian R. Porteous |
| title_short | Clifford algebras and the classical groups |
| title_sort | clifford algebras and the classical groups |
| topic | Clifford algebras Group theory Gruppentheorie (DE-588)4072157-7 gnd Topologische Geometrie (DE-588)4330788-7 gnd Clifford-Algebra (DE-588)4199958-7 gnd Lie-Gruppe (DE-588)4035695-4 gnd |
| topic_facet | Clifford algebras Group theory Gruppentheorie Topologische Geometrie Clifford-Algebra Lie-Gruppe |
| url | https://doi.org/10.1017/CBO9780511470912 |
| work_keys_str_mv | AT porteousianr cliffordalgebrasandtheclassicalgroups AT porteousianr cliffordalgebrastheclassicalgroups |