On quaternions and octonions :: their geometry, arithmetic, and symmetry /
"This book investigates the geometry of quaternion and octonion algebras. Following a comprehensive historical introduction, the book illuminates the special properties of 3- and 4-dimensional Euclidean spaces using quaternions, leading to enumerations of the corresponding finite groups of symm...
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Weitere Verfasser: | |
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Natick, Mass. :
AK Peters,
©2003.
|
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Zusammenfassung: | "This book investigates the geometry of quaternion and octonion algebras. Following a comprehensive historical introduction, the book illuminates the special properties of 3- and 4-dimensional Euclidean spaces using quaternions, leading to enumerations of the corresponding finite groups of symmetries. The second half of the book discusses the less familiar octonion algebra, concentrating on its remarkable "triality symmetry" after an appropriate study of Moufang loops. The authors also describe the arithmetics of the quaternions and octonions. The book concludes with a new theory of octonion factorization. Topics covered include the geometry of complex numbers, quaternions and 3-dimensional groups, quaternions and 4-dimensional groups, Hurwitz integral quaternions, composition algebras, Moufang loops, octonions and 8-dimensional geometry, integral octonions, and the octonion projective plane."--Provided by publisher. |
| Beschreibung: | 1 online resource (xii, 159 pages) : illustrations |
| Bibliographie: | Includes bibliographical references (pages 149-152) and index. |
| ISBN: | 9781439864180 1439864187 1568811349 9781568811345 0429185863 9780429185861 1000687775 9781000687774 |
Internformat
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| 245 | 1 | 0 | |a On quaternions and octonions : |b their geometry, arithmetic, and symmetry / |c John H. Conway, Derek A. Smith. |
| 260 | |a Natick, Mass. : |b AK Peters, |c ©2003. | ||
| 300 | |a 1 online resource (xii, 159 pages) : |b illustrations | ||
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| 504 | |a Includes bibliographical references (pages 149-152) and index. | ||
| 588 | 0 | |a Print version record. | |
| 505 | 0 | |a The complex numbers -- The quaternions -- The octonions. | |
| 546 | |a English. | ||
| 520 | 2 | |a "This book investigates the geometry of quaternion and octonion algebras. Following a comprehensive historical introduction, the book illuminates the special properties of 3- and 4-dimensional Euclidean spaces using quaternions, leading to enumerations of the corresponding finite groups of symmetries. The second half of the book discusses the less familiar octonion algebra, concentrating on its remarkable "triality symmetry" after an appropriate study of Moufang loops. The authors also describe the arithmetics of the quaternions and octonions. The book concludes with a new theory of octonion factorization. Topics covered include the geometry of complex numbers, quaternions and 3-dimensional groups, quaternions and 4-dimensional groups, Hurwitz integral quaternions, composition algebras, Moufang loops, octonions and 8-dimensional geometry, integral octonions, and the octonion projective plane."--Provided by publisher. | |
| 650 | 0 | |a Quaternions. |0 http://id.loc.gov/authorities/subjects/sh85109754 | |
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| 650 | 6 | |a Quaternions. | |
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| 650 | 7 | |a Quaternion. |2 rasuqam | |
| 650 | 7 | |a Octonion. |2 rasuqam | |
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| _version_ | 1816881707410784256 |
| adam_text | |
| any_adam_object | |
| author | Conway, John H. (John Horton) |
| author2 | Smith, Derek Alan, 1970- |
| author2_role | |
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| author_GND | http://id.loc.gov/authorities/names/n82119161 http://id.loc.gov/authorities/names/no99053182 |
| author_facet | Conway, John H. (John Horton) Smith, Derek Alan, 1970- |
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| contents | The complex numbers -- The quaternions -- The octonions. |
| ctrlnum | (OCoLC)560284450 |
| dewey-full | 512/.5 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
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| dewey-search | 512/.5 |
| dewey-sort | 3512 15 |
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| discipline | Mathematik |
| format | Electronic eBook |
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| genre | Electronic book. |
| genre_facet | Electronic book. |
| id | ZDB-4-EBA-ocn560284450 |
| illustrated | Illustrated |
| indexdate | 2024-11-27T13:17:00Z |
| institution | BVB |
| isbn | 9781439864180 1439864187 1568811349 9781568811345 0429185863 9780429185861 1000687775 9781000687774 |
| language | English |
| oclc_num | 560284450 |
| open_access_boolean | |
| owner | MAIN DE-863 DE-BY-FWS |
| owner_facet | MAIN DE-863 DE-BY-FWS |
| physical | 1 online resource (xii, 159 pages) : illustrations |
| psigel | ZDB-4-EBA |
| publishDate | 2003 |
| publishDateSearch | 2003 |
| publishDateSort | 2003 |
| publisher | AK Peters, |
| record_format | marc |
| spelling | Conway, John H. (John Horton) https://id.oclc.org/worldcat/entity/E39PBJj4p9yb39QkgPGr4wMHG3 http://id.loc.gov/authorities/names/n82119161 On quaternions and octonions : their geometry, arithmetic, and symmetry / John H. Conway, Derek A. Smith. Natick, Mass. : AK Peters, ©2003. 1 online resource (xii, 159 pages) : illustrations text txt rdacontent computer c rdamedia online resource cr rdacarrier data file Includes bibliographical references (pages 149-152) and index. Print version record. The complex numbers -- The quaternions -- The octonions. English. "This book investigates the geometry of quaternion and octonion algebras. Following a comprehensive historical introduction, the book illuminates the special properties of 3- and 4-dimensional Euclidean spaces using quaternions, leading to enumerations of the corresponding finite groups of symmetries. The second half of the book discusses the less familiar octonion algebra, concentrating on its remarkable "triality symmetry" after an appropriate study of Moufang loops. The authors also describe the arithmetics of the quaternions and octonions. The book concludes with a new theory of octonion factorization. Topics covered include the geometry of complex numbers, quaternions and 3-dimensional groups, quaternions and 4-dimensional groups, Hurwitz integral quaternions, composition algebras, Moufang loops, octonions and 8-dimensional geometry, integral octonions, and the octonion projective plane."--Provided by publisher. Quaternions. http://id.loc.gov/authorities/subjects/sh85109754 Cayley numbers (Algebra) http://id.loc.gov/authorities/subjects/sh2002008702 Quaternions. Cayley, Octaves de. MATHEMATICS Algebra Intermediate. bisacsh Cayley numbers (Algebra) fast Quaternions fast Quaternionenalgebra gnd http://d-nb.info/gnd/4618620-7 Cayley-Zahlen gnd http://d-nb.info/gnd/4745179-8 Algebraische Geometrie gnd http://d-nb.info/gnd/4001161-6 Quaternios. larpcal Álgebra. larpcal Quaternion. rasuqam Octonion. rasuqam Electronic book. Smith, Derek Alan, 1970- https://id.oclc.org/worldcat/entity/E39PCjt8RyvmWtFr8gGfYmY4C3 http://id.loc.gov/authorities/names/no99053182 has work: On quaternions and octonions (Text) https://id.oclc.org/worldcat/entity/E39PCG463DQgkvD47xgC4wwDdP https://id.oclc.org/worldcat/ontology/hasWork Print version: Conway, John Horton. On quaternions and octonions. Natick, Mass. : AK Peters, ©2003 1568811349 9781568811345 (DLC) 2002035555 (OCoLC)50761334 FWS01 ZDB-4-EBA FWS_PDA_EBA https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=1802333 Volltext |
| spellingShingle | Conway, John H. (John Horton) On quaternions and octonions : their geometry, arithmetic, and symmetry / The complex numbers -- The quaternions -- The octonions. Quaternions. http://id.loc.gov/authorities/subjects/sh85109754 Cayley numbers (Algebra) http://id.loc.gov/authorities/subjects/sh2002008702 Quaternions. Cayley, Octaves de. MATHEMATICS Algebra Intermediate. bisacsh Cayley numbers (Algebra) fast Quaternions fast Quaternionenalgebra gnd http://d-nb.info/gnd/4618620-7 Cayley-Zahlen gnd http://d-nb.info/gnd/4745179-8 Algebraische Geometrie gnd http://d-nb.info/gnd/4001161-6 Quaternios. larpcal Álgebra. larpcal Quaternion. rasuqam Octonion. rasuqam |
| subject_GND | http://id.loc.gov/authorities/subjects/sh85109754 http://id.loc.gov/authorities/subjects/sh2002008702 http://d-nb.info/gnd/4618620-7 http://d-nb.info/gnd/4745179-8 http://d-nb.info/gnd/4001161-6 |
| title | On quaternions and octonions : their geometry, arithmetic, and symmetry / |
| title_auth | On quaternions and octonions : their geometry, arithmetic, and symmetry / |
| title_exact_search | On quaternions and octonions : their geometry, arithmetic, and symmetry / |
| title_full | On quaternions and octonions : their geometry, arithmetic, and symmetry / John H. Conway, Derek A. Smith. |
| title_fullStr | On quaternions and octonions : their geometry, arithmetic, and symmetry / John H. Conway, Derek A. Smith. |
| title_full_unstemmed | On quaternions and octonions : their geometry, arithmetic, and symmetry / John H. Conway, Derek A. Smith. |
| title_short | On quaternions and octonions : |
| title_sort | on quaternions and octonions their geometry arithmetic and symmetry |
| title_sub | their geometry, arithmetic, and symmetry / |
| topic | Quaternions. http://id.loc.gov/authorities/subjects/sh85109754 Cayley numbers (Algebra) http://id.loc.gov/authorities/subjects/sh2002008702 Quaternions. Cayley, Octaves de. MATHEMATICS Algebra Intermediate. bisacsh Cayley numbers (Algebra) fast Quaternions fast Quaternionenalgebra gnd http://d-nb.info/gnd/4618620-7 Cayley-Zahlen gnd http://d-nb.info/gnd/4745179-8 Algebraische Geometrie gnd http://d-nb.info/gnd/4001161-6 Quaternios. larpcal Álgebra. larpcal Quaternion. rasuqam Octonion. rasuqam |
| topic_facet | Quaternions. Cayley numbers (Algebra) Cayley, Octaves de. MATHEMATICS Algebra Intermediate. Quaternions Quaternionenalgebra Cayley-Zahlen Algebraische Geometrie Quaternios. Álgebra. Quaternion. Octonion. Electronic book. |
| url | https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=1802333 |
| work_keys_str_mv | AT conwayjohnh onquaternionsandoctonionstheirgeometryarithmeticandsymmetry AT smithderekalan onquaternionsandoctonionstheirgeometryarithmeticandsymmetry |