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Journal of Lie Theory, Vol. 10, No. 2, pp. 375-381 (2000)
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Compactification structure and conformal compressions of symmetric cones

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Jimmie D. Lawson and Yongdo Lim

Jimmie d. Lawson

Department of Mathematics

Louisiana State University

Baton Rouge La 70803, U.S.A.

and

Yongdo Lim

Research Center

Kyungpook National University

Taegu 702-701, Korea

**Abstract:** In this paper we show that the boundary of a symmetric cone $\Omega$ in the standard real conformal compactification $\M$ of its containing euclidean Jordan algebra $V$ has the structure of a double cone, with the points at infinity forming one of the cones. We further show that ${\overline\Omega}^{\M}$ admits a natural partial order extending that of $\Omega$. Each element of the compression semigroup for $\Omega$ is shown to act in an order-preserving way on ${\overline\Omega}^{\M}$ and carries it into an order interval contained in ${\overline\Omega}^{\M}$.

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