153 research outputs found
Angular Momentum, Quaternion, Octonion, and Lie-Super Algebra osp(1,2)
We will derive both quaternion and octonion algebras as the Clebsch-Gordan
algebras based upon the su(2) Lie algebra by considering angular momentum
spaces of spin one and three. If we consider both spin 1 and 1/2 states, then
the same method will lead to the Lie-super algebra osp(1,2). Also, the quantum
generalization of the method is discussed on the basis of the quantum group
.Comment: 17 pages, TE
Construction of Lie Superalgebras from Triple Product Systems
Any simple Lie superalgebras over the complex field can be constructed from
some triple systems. Examples of Lie superalgebras , G(3) and
F(4) are given by utilizing a general construction method based upon
balanced Freudenthal-Kantor triple system.Comment: 8 pages, no figure
Triple Products and Yang-Baxter Equation (I): Octonionic and Quaternionic Triple Systems
We can recast the Yang-Baxter equation as a triple product equation. Assuming
the triple product to satisfy some algebraic relations, we can find new
solutions of the Yang-Baxter equation. This program has been completed here for
the simplest triple systems which we call octonionic and quaternionic. The
solutions are of rational type.Comment: 29 page
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