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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Published in:Symmetry, Integrability and Geometry: Methods and Applications
Date:2007
Main Author: McRae, A.S.
Format: Article
Language:English
Published: Інститут математики НАН України 2007
Online Access:https://nasplib.isofts.kiev.ua/handle/123456789/147367
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Journal Title:Digital Library of Periodicals of National Academy of Sciences of Ukraine
Cite this: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
id nasplib_isofts_kiev_ua-123456789-147367
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
institution Digital Library of Periodicals of National Academy of Sciences of Ukraine
collection DSpace DC
title Clifford Algebras and Possible Kinematics
spellingShingle Clifford Algebras and Possible Kinematics
McRae, A.S.
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
author McRae, A.S.
author_facet McRae, A.S.
publishDate 2007
language English
container_title Symmetry, Integrability and Geometry: Methods and Applications
publisher Інститут математики НАН України
format Article
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.
issn 1815-0659
url https://nasplib.isofts.kiev.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.
work_keys_str_mv AT mcraeas cliffordalgebrasandpossiblekinematics
first_indexed 2025-11-30T16:09:37Z
last_indexed 2025-11-30T16:09:37Z
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