Jordan and isometric cone automorphisms in Euclidean Jordan algebras

Every symmetric cone K arises as the cone of squares in a Euclidean Jordan algebra V. As V is a real inner-product space, we may denote by Isom(V) its group of isometries. The groups JAut(V) of its Jordan-algebra automorphisms and Aut(K) of the linear cone automorphisms are then related. For certain inner products, JAut(V) = Aut(K) ∩ Isom(V). We characterize the inner products for which this holds.

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