Clifford Algebras and Possible Kinematics
We review Bacry and Lévy-Leblond's work on possible kinematics as applied to 2-dimensional spacetimes, as well as the nine types of 2-dimensional Cayley-Klein geometries, illustrating how the Cayley-Klein geometries give homogeneous spacetimes for all but one of the kinematical groups. We then...
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| Опубліковано в: : | Symmetry, Integrability and Geometry: Methods and Applications |
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| Дата: | 2007 |
| Автор: | |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Інститут математики НАН України
2007
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| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/147367 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Clifford Algebras and Possible Kinematics / A.S. McRae // Symmetry, Integrability and Geometry: Methods and Applications. — 2007. — Т. 3. — Бібліогр.: 28 назв. — англ. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862634426565918720 |
|---|---|
| author | McRae, A.S. |
| author_facet | McRae, A.S. |
| citation_txt | Clifford Algebras and Possible Kinematics / A.S. McRae // Symmetry, Integrability and Geometry: Methods and Applications. — 2007. — Т. 3. — Бібліогр.: 28 назв. — англ. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | We review Bacry and Lévy-Leblond's work on possible kinematics as applied to 2-dimensional spacetimes, as well as the nine types of 2-dimensional Cayley-Klein geometries, illustrating how the Cayley-Klein geometries give homogeneous spacetimes for all but one of the kinematical groups. We then construct a two-parameter family of Clifford algebras that give a unified framework for representing both the Lie algebras as well as the kinematical groups, showing that these groups are true rotation groups. In addition we give conformal models for these spacetimes.
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| first_indexed | 2025-11-30T16:09:37Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-147367 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-11-30T16:09:37Z |
| publishDate | 2007 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | McRae, A.S. 2019-02-14T14:45:50Z 2019-02-14T14:45:50Z 2007 Clifford Algebras and Possible Kinematics / A.S. McRae // Symmetry, Integrability and Geometry: Methods and Applications. — 2007. — Т. 3. — Бібліогр.: 28 назв. — англ. 1815-0659 2000 Mathematics Subject Classification: 11E88; 15A66; 53A17 https://nasplib.isofts.kiev.ua/handle/123456789/147367 We review Bacry and Lévy-Leblond's work on possible kinematics as applied to 2-dimensional spacetimes, as well as the nine types of 2-dimensional Cayley-Klein geometries, illustrating how the Cayley-Klein geometries give homogeneous spacetimes for all but one of the kinematical groups. We then construct a two-parameter family of Clifford algebras that give a unified framework for representing both the Lie algebras as well as the kinematical groups, showing that these groups are true rotation groups. In addition we give conformal models for these spacetimes. I wish to thank the referees for their careful reading of this paper and their suggestions for
 valuable improvements. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Clifford Algebras and Possible Kinematics Article published earlier |
| spellingShingle | Clifford Algebras and Possible Kinematics McRae, A.S. |
| title | Clifford Algebras and Possible Kinematics |
| title_full | Clifford Algebras and Possible Kinematics |
| title_fullStr | Clifford Algebras and Possible Kinematics |
| title_full_unstemmed | Clifford Algebras and Possible Kinematics |
| title_short | Clifford Algebras and Possible Kinematics |
| title_sort | clifford algebras and possible kinematics |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/147367 |
| work_keys_str_mv | AT mcraeas cliffordalgebrasandpossiblekinematics |