Octonions and Super Lie algebra
Khaled Abdel-Khalek (Phys. Dept./Lecce Univ.)
TL;DR
This paper explores representing octonions within matrix algebra, constructs Lie and Super Lie algebras explicitly, and discusses octonionic Grassmann numbers for supersymmetric Yang-Mills models.
Contribution
It introduces a method to represent octonionic structures via associative matrices and applies this to construct Lie and Super Lie algebras, proposing a new approach for superspace formulations.
Findings
Explicit construction of Lie and Super Lie algebras using octonionic operators
Introduction of octonionic Grassmann numbers for supersymmetric theories
Potential application to superspace formulation of minimal supersymmetric Yang-Mills models
Abstract
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.
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