TL;DR
This paper reviews quaternionic and octonionic spinors, analyzes their Dirac equations, constructs related supersymmetric algebras, and discusses their relation to M-theory in eleven dimensions.
Contribution
It introduces and explores the properties of quaternionic and octonionic spinors, including their associated supersymmetric algebras and connections to M-theory.
Findings
Quaternionic and octonionic spinors are supported in specific space-times.
Conditions for Dirac equations with these spinors are established.
Relations between quaternionic/octonionic supersymmetries and M-algebra are discussed.
Abstract
Quaternionic and octonionic spinors are introduced and their fundamental properties (such as the space-times supporting them) are reviewed. The conditions for the existence of their associated Dirac equations are analyzed. Quaternionic and octonionic supersymmetric algebras defined in terms of such spinors are constructed. Specializing to the D=11-dimensional case, the relation of both the quaternionic and the octonionic supersymmetries with the ordinary M-algebra are discussed.
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