Octonions and Super Lie algebra

We discuss how to represent the non-associative octonionic structure in terms of the associative matrix algebra using the left and right octonionic operators. As an example we construct explicitly some Lie and Super Lie algebra. Then we discuss the notion of octonionic Grassmann numbers and explain its possible application for giving a superspace formulation of the minimal supersymmetric Yang-Mills models.Comment: RevTex file, 12 pages, to be published in Int. J. of Mod. Phys. A; Some references adde

Octonionic Quantum Mechanics and Complex Geometry

The use of complex geometry allows us to obtain a consistent formulation of octonionic quantum mechanics (OQM). In our octonionic formulation we solve the hermiticity problem and define an appropriate momentum operator within OQM. The nonextendability of the completeness relation and the norm conservation is also discussed in details.Comment: To appear in Prog. Theor. Phys. (vol 96