Conformal transformations and Clifford algebras
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- by Pertti Lounesto and Esko Latvamaa
- Proc. Amer. Math. Soc. 79 (1980), 533-538
- DOI: https://doi.org/10.1090/S0002-9939-1980-0572296-4
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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.References
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Bibliographic Information
- © Copyright 1980 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 79 (1980), 533-538
- MSC: Primary 15A66; Secondary 81C40
- DOI: https://doi.org/10.1090/S0002-9939-1980-0572296-4
- MathSciNet review: 572296