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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Conformal transformations and Clifford algebras


Authors: Pertti Lounesto and Esko Latvamaa
Journal: Proc. Amer. Math. Soc. 79 (1980), 533-538
MSC: Primary 15A66; Secondary 81C40
MathSciNet review: 572296
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Abstract: A spinor representation for the conformal group of the real orthogonal space $ {R^{p,q}}$ is given. First, the real orthogonal space $ {R^{p,q}}$ is compactified by adjoining a (closed) isotropic cone at infinity. Then the nonlinear conformal transformations are linearized by regarding the conformal group as a factor group of a larger orthogonal group. Finally, the spin covering group of this larger orthogonal group is realized in the Clifford algebra $ {R_{1 + p,q}}$ containing the Clifford algebra $ {R_{p,q}}$ on the orthogonal space $ {R^{p,q}}$. Explicit formulas for orthogonal transformations, translations, dilatations and special conformal transformations are given in Clifford language.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1980-0572296-4
PII: S 0002-9939(1980)0572296-4
Article copyright: © Copyright 1980 American Mathematical Society