Jordan and isometric cone automorphisms in Euclidean Jordan algebras

Key Points

• The study reveals that certain inner products allow the group of jordan-algebra automorphisms to coincide with linear cone automorphisms.
• It identifies the conditions under which the jordan-algebra automorphisms are contained within the group of isometries.
• Understanding the structure of symmetric cones can aid in the classification of euclidean jordan algebras.
• These findings offer new insights into the interplay between geometrical properties and algebraic structures in Euclidean spaces.