Some P-properties of the Quadratic Representations and Automorphism Invariance in Euclidean Jordan Algebras

Quadratic representations are very useful in the study of Euclidean Jordan algebras and complementarity problems. In this paper, we provide some characterizations of the complementarity properties for the quadratic representation P a . For example, P a has the E 0 -property; P a is monotone iff ± a ∈ K . In addition, the algebra and cone automorphism invariance of some E-properties are studied. By use of the quadratic representations, the Jordan quad E-property is proved to keep cone automorphism invariant in simple Jordan algebras. The pseudomonotone property is shown to be cone automorphism invariant.