Abstract
A pseudo-euclidean Jordan algebra is a Jordan algebra with an associative non-degenerate symmetric bilinear form B. We study the structure of the pseudo-euclideanJordan algebras over a field K of characteristic not two, and we obtain an inductivedescription of these algebras in terms of double extensions and generalized doubleextensions. Next, we study the symplectic pseudo-euclidean K-Jordan algebras, and wegive some informations on a particular class of these algebras, namely the class ofsymplectic Jordan–Manin Algebras.