  First, we study pseudo-Euclidean Jordan algebras obtained as double
extensions of a quadratic vector space by a one-dimensional algebra. We give an
isomorphic characterization of 2-step nilpotent pseudo-Euclidean Jordan
algebras. Next, we find a Jordan-admissible condition for a Novikov algebra
$\N$. Finally, we focus on the case of a symmetric Novikov algebra and study it
up to dimension 7.
