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Symmetry, Integrability and Geometry: Methods and Applications, 2007, Volume 3, 079, 29 pp.
DOI: https://doi.org/10.3842/SIGMA.2007.079
(Mi sigma205)
 

This article is cited in 8 scientific papers (total in 8 papers)

Clifford Algebras and Possible Kinematics

Alan S. McRae

Department of Mathematics, Washington and Lee University, Lexington, VA 24450-0303, USA
Full-text PDF (571 kB) Citations (8)
References:
Abstract: 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.
Keywords: Cayley–Klein geometries; Clifford algebras; kinematics.
Received: April 30, 2007; in final form July 3, 2007; Published online July 19, 2007
Bibliographic databases:
Document Type: Article
MSC: 11E88; 15A66; 53A17
Language: English
Citation: Alan S. McRae, “Clifford Algebras and Possible Kinematics”, SIGMA, 3 (2007), 079, 29 pp.
Citation in format AMSBIB
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  • This publication is cited in the following 8 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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