ABSTRACT
Abstract Algebras satisfying symmetric triality relations are shown to lead to a construction of Lie algebras that will give Freudenthal’s magic square. Some examples of these algebras are given and studied. Keywords: symmetric triality algebra, nonassociative algebras, structurable algebras, Freundenthal’s magic square 2000 MSC: 17B25; 17A75
Recently, Burton and Sudbery [2] reformulated the standard construction of exceptional Lie algebras by Tit [11] as a construction using two composition algebras. Subsequently, a more symmetrical approach has been found by Elduque [3] in terms of symmetric triality relations based upon two symmetric composition algebras.
