In particular, we describe primitive Jordan pairs and triple systems over an arbitrary ring of scalars in the sense of “The Structure of Primitive Quadratic Jordan Algebras” by J. A. Anquela, T. Cortés, and F. Montaner (1995, J. Algebra 172, 530–553, 5.1). Previous article in issue Next article in issueThe particular approach to e 8 described in a unification model formulated in 2007 by Lisi [Li] (later discovered to contain various issues [DG]), inspired Truini to rigorously investigate a special star-like projection -named "Magic Star" -of e 8 under This led to a unified construction and characterization of all exceptional Lie algebras, filling the fourth row of the Freudenthal-Rozen-Tits Magic Square [MS]. Jordan algebras introduced by Kevin McCrimmon (1966). The fundamental identities of the quadratic representation of a linear Jordan algebra are used as axioms to define a quadratic Jordan algebra over a field of arbitrary characteristic.where is a complex *-algebra and are unknown additive functions. This problem arises naturally in connection with the question of representability of quadratic It begins with the general theory of nonassociative algebras and of Lie algebras and then ... Zelmanov's seminal results on infinite-dimensional Lie algebras from this point of view. ... The definitions of Lie algebras and Jordan algebras are provided, rather than ... From Lie Algebras to Jordan Pairs