Multiplicatively Ordered and Directed Hybrid Jordan-Lie Superalgebra

A new algebra, hitherto not encountered in the usual Lie algebraic varieties or supervarieties, is introduced. The paper explores the rich and novel structure of the algebra, and it compares it on the one hand with the Jordan-Lie Superalgebras studied by Okubo and Kamiya, and on the other, with the four usual Euclidean division rings of the reals, the complexes, the quaternions and the octonions that the algebra is seen to combine, extend and generalise. A potential physical application of the algebra is briefly alluded to at the end.