Clifford algebras: an introduction
Clifford algebras, built up from quadratic spaces, have applications in many areas of mathematics, as natural generalizations of complex numbers and the quaternions. They are famously used in proofs of the Atiyah–Singer index theorem, to provide double covers (spin groups) of the classical groups an...
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| Main Author: | |
|---|---|
| Format: | Electronic eBook |
| Language: | English |
| Published: |
Cambridge
Cambridge University Press
2011
|
| Series: | London Mathematical Society student texts
78 |
| Subjects: | |
| Online Access: | BSB01 FHN01 UBR01 Volltext |
| Summary: | Clifford algebras, built up from quadratic spaces, have applications in many areas of mathematics, as natural generalizations of complex numbers and the quaternions. They are famously used in proofs of the Atiyah–Singer index theorem, to provide double covers (spin groups) of the classical groups and to generalize the Hilbert transform. They also have their place in physics, setting the scene for Maxwell's equations in electromagnetic theory, for the spin of elementary particles and for the Dirac equation. This straightforward introduction to Clifford algebras makes the necessary algebraic background - including multilinear algebra, quadratic spaces and finite-dimensional real algebras - easily accessible to research students and final-year undergraduates. The author also introduces many applications in mathematics and physics, equipping the reader with Clifford algebras as a working tool in a variety of contexts |
| Physical Description: | 1 Online-Ressource (vii, 200 Seiten) |
| ISBN: | 9780511972997 |
| DOI: | 10.1017/CBO9780511972997 |
Staff View
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| spelling | Garling, David J. H. 1937- Verfasser (DE-588)1013706781 aut Clifford algebras an introduction D.J.H. Garling Cambridge Cambridge University Press 2011 1 Online-Ressource (vii, 200 Seiten) txt rdacontent c rdamedia cr rdacarrier London Mathematical Society student texts 78 Clifford algebras, built up from quadratic spaces, have applications in many areas of mathematics, as natural generalizations of complex numbers and the quaternions. They are famously used in proofs of the Atiyah–Singer index theorem, to provide double covers (spin groups) of the classical groups and to generalize the Hilbert transform. They also have their place in physics, setting the scene for Maxwell's equations in electromagnetic theory, for the spin of elementary particles and for the Dirac equation. This straightforward introduction to Clifford algebras makes the necessary algebraic background - including multilinear algebra, quadratic spaces and finite-dimensional real algebras - easily accessible to research students and final-year undergraduates. The author also introduces many applications in mathematics and physics, equipping the reader with Clifford algebras as a working tool in a variety of contexts Clifford algebras Clifford-Algebra (DE-588)4199958-7 gnd rswk-swf 1\p (DE-588)4151278-9 Einführung gnd-content Clifford-Algebra (DE-588)4199958-7 s DE-604 Erscheint auch als Druck-Ausgabe 978-1-107-09638-7 Erscheint auch als Druck-Ausgabe 978-1-107-42219-3 https://doi.org/10.1017/CBO9780511972997 Verlag URL des Erstveröffentlichers Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Garling, David J. H. 1937- Clifford algebras an introduction Clifford algebras Clifford-Algebra (DE-588)4199958-7 gnd |
| subject_GND | (DE-588)4199958-7 (DE-588)4151278-9 |
| title | Clifford algebras an introduction |
| title_auth | Clifford algebras an introduction |
| title_exact_search | Clifford algebras an introduction |
| title_full | Clifford algebras an introduction D.J.H. Garling |
| title_fullStr | Clifford algebras an introduction D.J.H. Garling |
| title_full_unstemmed | Clifford algebras an introduction D.J.H. Garling |
| title_short | Clifford algebras |
| title_sort | clifford algebras an introduction |
| title_sub | an introduction |
| topic | Clifford algebras Clifford-Algebra (DE-588)4199958-7 gnd |
| topic_facet | Clifford algebras Clifford-Algebra Einführung |
| url | https://doi.org/10.1017/CBO9780511972997 |
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