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Analysis of the relationship between jordan-algebra automorphisms and isometries in symmetric cones.
Every symmetric cone K arises as the cone of squares in aEuclidean Jordan algebra V. As V is a real inner-productspace, we may denote by Isom(V) its group of isometries. Thegroups JAut(V) of its Jordan-algebra automorphisms andAut(K) of the linear cone automorphisms are then related. Forcertain inner products,{equation*}JAut(V)=Aut(K) ∩ Isom(V).{equation*}We characterize the inner products for which this holds.
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Michael Orlitzky (2025) studied this question.
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