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Symmetric geodesics on conformal compactifications of Euclidean Jordan algebras

Published online by Cambridge University Press:  17 April 2009

Sang Youl Lee ,
Yongdo Lim  and
Chan-Young Park
Sang Youl Lee
Affiliation:
Department of Mathematics, College of Natural Sciences, Kyungpook National University, Taegu 702-701, Korea e-mail: [email protected]
Yongdo Lim
Affiliation:
Topology and Geometry Research Center, Kyungpook National University, Taegu 702-701, Korea e-mail: [email protected]
Chan-Young Park
Affiliation:
Department of Mathematics, College of Natural Sciences, Kyungpook National University, Taegu 702-701, Korea e-mail: [email protected]
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Abstract

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In this article we define symmetric geodesies on conformal compactifications of Euclidean Jordan algebras and classify symmetric geodesics for the Euclidean Jordan algebra of all n × n symmetric real matrices. Furthermore, we show that the closed geodesics for the Euclidean Jordan algebra of all 2 × 2 symmetric real matrices are realised as the torus knots in the Shilov boundary of a Lie ball.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 59 , Issue 2 , April 1999 , pp. 187 - 201
Copyright
Copyright © Australian Mathematical Society 1999

References

[1]Bertram, W., ‘Un théorè;me de Liouville pour les algèbres de Jordan’, Bull. Soc. Math. France 124 (1996), 299–327.Google Scholar
[2]Bertram, W., ‘On some classes and conformal groups’, J. Lie Theory 6 (1996), 215–247.Google Scholar
[3]Bertram, W., ‘Algebraic structures of Makarevič spaces I’, Transform. Groups 1 (1998), 3–32.CrossRefGoogle Scholar
[4]Faraut, J. and Koranyi, A., Analysis on symmetric cones, Oxford Mathematical Monographs (Oxford University Press, Oxford, 1994).CrossRefGoogle Scholar
[5]Hilgert, J. and Olafsson, G., Causal symmetric spaces. Geometry and harmonic analysis, Perspectives in Mathematics 18 (Academic Press, San Diego, 1997).Google Scholar
[6]Kaup, W., ‘Algebraic characterization of symmetric complex Banach manifolds’, Math. Ann. 228 (1977), 39–64.CrossRefGoogle Scholar
[7]Kaup, W., ‘A Riemann mapping theorem for bounded symmetric domains in complex banach spaces’, Math. Z. 183 (1983), 503–529.CrossRefGoogle Scholar
[8]Koufany, K., ‘Semi-groupe de Lie associé a un cône symétriques’, Ann. Inst. Fourier (Grenoble) 45 (1995), 1–29.CrossRefGoogle Scholar
[9]Lawson, J.D. and Lim, Y., ‘Lie semigroups with triple decompositions’, (submitted).Google Scholar
[10]Loos, O., Bounded symmetric domains and Jordan pairs, Lecture Notes (University California, Irvine 1977).Google Scholar
[11]Makarevič, B. ‘Ideal points of semisimple Jordan algebras’, Mat. Zametki 15 (1974), 295–305.Google Scholar
[12]Rolfsen, D., Knots and links, Mathematics Lecture Series 7 (Publish or Perish Press, Berkley, CA, 1976).Google Scholar