Clifford Algebras and Possible Kinematics

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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Дата:2007
Автор: McRae, A.S.
Формат: Стаття
Мова:English
Опубліковано: Інститут математики НАН України 2007
Назва видання:Symmetry, Integrability and Geometry: Methods and Applications
Онлайн доступ:http://dspace.nbuv.gov.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.

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Digital Library of Periodicals of National Academy of Sciences of Ukraine
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spelling irk-123456789-1473672019-02-15T01:23:13Z Clifford Algebras and Possible Kinematics McRae, A.S. 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. 2007 Article 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 http://dspace.nbuv.gov.ua/handle/123456789/147367 en Symmetry, Integrability and Geometry: Methods and Applications Інститут математики НАН України
institution Digital Library of Periodicals of National Academy of Sciences of Ukraine
collection DSpace DC
language English
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.
format Article
author McRae, A.S.
spellingShingle McRae, A.S.
Clifford Algebras and Possible Kinematics
Symmetry, Integrability and Geometry: Methods and Applications
author_facet McRae, A.S.
author_sort McRae, A.S.
title Clifford Algebras and Possible Kinematics
title_short 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_sort clifford algebras and possible kinematics
publisher Інститут математики НАН України
publishDate 2007
url http://dspace.nbuv.gov.ua/handle/123456789/147367
citation_txt Clifford Algebras and Possible Kinematics / A.S. McRae // Symmetry, Integrability and Geometry: Methods and Applications. — 2007. — Т. 3. — Бібліогр.: 28 назв. — англ.
series Symmetry, Integrability and Geometry: Methods and Applications
work_keys_str_mv AT mcraeas cliffordalgebrasandpossiblekinematics
first_indexed 2023-05-20T17:27:10Z
last_indexed 2023-05-20T17:27:10Z
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