Journal of Lie Theory
Vol. 9, No. 1, pp. 203-213 (1999)

Transformation Groups of the Andersson-Perlman Cone

E. Neher

Department of Mathematics and Statistics
University of Ottawa
Ottawa, Ontario K1N 6N5

Abstract: An Andersson-Perlman cone is a certain subcone ${\scriptstyle O({\cal K})}$ of the symmetric cone $\scriptstyle O$ of a Euclidean Jordan algebra. We exhibit a subgroup of the automorphism group of ${\scriptstyle O}$ which operates transitively on ${\scriptstyle O({\cal K})}$ and show that ${\scriptstyle O({\cal K})}$ is a simply-connected submanifold of $\scriptstyle O$.

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