Clifford Fibrations and Possible Kinematics
Following Herranz and Santander [Herranz F.J., Santander M., Mem. Real Acad. Cienc. Exact. Fis. Natur. Madrid 32 (1998), 59-84, physics/9702030] we will construct homogeneous spaces based on possible kinematical algebras and groups [Bacry H., Levy-Leblond J.-M., J. Math. Phys. 9 (1967), 1605-1614] a...
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| Опубліковано в: : | Symmetry, Integrability and Geometry: Methods and Applications |
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| Дата: | 2009 |
| Автор: | |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Інститут математики НАН України
2009
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| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/149149 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Clifford Fibrations and Possible Kinematics / A.S. McRae // Symmetry, Integrability and Geometry: Methods and Applications. — 2009. — Т. 5. — Бібліогр.: 12 назв. — англ. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862729635383476224 |
|---|---|
| author | McRae, A.S. |
| author_facet | McRae, A.S. |
| citation_txt | Clifford Fibrations and Possible Kinematics / A.S. McRae // Symmetry, Integrability and Geometry: Methods and Applications. — 2009. — Т. 5. — Бібліогр.: 12 назв. — англ. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | Following Herranz and Santander [Herranz F.J., Santander M., Mem. Real Acad. Cienc. Exact. Fis. Natur. Madrid 32 (1998), 59-84, physics/9702030] we will construct homogeneous spaces based on possible kinematical algebras and groups [Bacry H., Levy-Leblond J.-M., J. Math. Phys. 9 (1967), 1605-1614] and their contractions for 2-dimensional spacetimes. Our construction is different in that it is based on a generalized Clifford fibration: Following Penrose [Penrose R., Alfred A. Knopf, Inc., New York, 2005] we will call our fibration a Clifford fibration and not a Hopf fibration, as our fibration is a geometrical construction. The simple algebraic properties of the fibration describe the geometrical properties of the kinematical algebras and groups as well as the spacetimes that are derived from them. We develop an algebraic framework that handles all possible kinematic algebras save one, the static algebra.
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| first_indexed | 2025-12-07T19:15:30Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-149149 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-07T19:15:30Z |
| publishDate | 2009 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | McRae, A.S. 2019-02-19T17:41:31Z 2019-02-19T17:41:31Z 2009 Clifford Fibrations and Possible Kinematics / A.S. McRae // Symmetry, Integrability and Geometry: Methods and Applications. — 2009. — Т. 5. — Бібліогр.: 12 назв. — англ. 1815-0659 2000 Mathematics Subject Classification: 11E88; 15A66; 53A17 https://nasplib.isofts.kiev.ua/handle/123456789/149149 Following Herranz and Santander [Herranz F.J., Santander M., Mem. Real Acad. Cienc. Exact. Fis. Natur. Madrid 32 (1998), 59-84, physics/9702030] we will construct homogeneous spaces based on possible kinematical algebras and groups [Bacry H., Levy-Leblond J.-M., J. Math. Phys. 9 (1967), 1605-1614] and their contractions for 2-dimensional spacetimes. Our construction is different in that it is based on a generalized Clifford fibration: Following Penrose [Penrose R., Alfred A. Knopf, Inc., New York, 2005] we will call our fibration a Clifford fibration and not a Hopf fibration, as our fibration is a geometrical construction. The simple algebraic properties of the fibration describe the geometrical properties of the kinematical algebras and groups as well as the spacetimes that are derived from them. We develop an algebraic framework that handles all possible kinematic algebras save one, the static algebra. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Clifford Fibrations and Possible Kinematics Article published earlier |
| spellingShingle | Clifford Fibrations and Possible Kinematics McRae, A.S. |
| title | Clifford Fibrations and Possible Kinematics |
| title_full | Clifford Fibrations and Possible Kinematics |
| title_fullStr | Clifford Fibrations and Possible Kinematics |
| title_full_unstemmed | Clifford Fibrations and Possible Kinematics |
| title_short | Clifford Fibrations and Possible Kinematics |
| title_sort | clifford fibrations and possible kinematics |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/149149 |
| work_keys_str_mv | AT mcraeas cliffordfibrationsandpossiblekinematics |