A binary encoding of spinors and applications

  title={A binary encoding of spinors and applications},
  author={Gerardo Arizmendi and Rafael Herrera},
  journal={Complex Manifolds},
  pages={162 - 193}
Abstract We present a binary code for spinors and Clifford multiplication using non-negative integers and their binary expressions, which can be easily implemented in computer programs for explicit calculations. As applications, we present explicit descriptions of the triality automorphism of Spin(8), explicit representations of the Lie algebras 𝔰𝔭𝔦𝔢 (8), 𝔰𝔭𝔦𝔢 (7) and 𝔀2, etc.Β 

Tables from this paper


Clifford Algebras and Spinors
A historical review of spinors is given together with a construction of spinor spaces as minimal left ideals of Clifford algebras. Spinor spaces of euclidean spaces over reals have a natural linear…
Fock space description of simple spinors
Cartan’s simpleβ€”often called pureβ€”spinors corresponding to even‐dimensional complex vector spaces are defined in terms of the associated maximal totally null planes. Their geometrical properties are…
Combinatorial construction of tangent vector fields on spheres
For every odd n, on the sphere Sn, ρ(n) βˆ’ 1 linear orthonormal tangent vector fields, where ρ(n) is the Hurwitz-Radon number, are explicitly constructed. For each 8 Γ— 8 sign matrix, compositions for…
Spinors and Calibrations
This paper presents a solution to the problem of finding the maximum number of linearly independent vector fields that can be placed on a sphere. To produce the correct upper bound, we make use of…
Octonions and triality
In this chapter, we explore another generalization of C and IE, a non-associative real algebra, the Cayley algebra of octonions, (D. Like complex numbers and quaternions, octonions f o r m a real…
Dirac Operators in Riemannian Geometry
Clifford algebras and spin representation Spin structures Dirac operators Analytical properties of Dirac operators Eigenvalue estimates for the Dirac operator and twistor spinors Seiberg-Witten…
Twistors and killing spinors on riemannian manifolds
The Octonions
The octonions are the largest of the four normed division algebras. While somewhat neglected due to their nonassociativity, they stand at the crossroads of many interesting fields of mathematics.…
Über die Komposition der quadratischen Formen