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 π°ππ¦πΆ (8), π°ππ¦πΆ (7) and π€2, etc.Β

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 linearβ¦ Expand

Cartanβs simpleβoften called pureβspinors corresponding to evenβdimensional complex vector spaces are defined in terms of the associated maximal totally null planes. Their geometrical properties areβ¦ Expand

For every odd n, on the sphere Sn, Ο(n) β 1 linear orthonormal tangent vector fields, where Ο(n) is the Hurwitz-Radon number, are explicitly constructed. For each 8 Γ 8 sign matrix, compositions forβ¦ Expand

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 ofβ¦ Expand

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 realβ¦ Expand

Clifford algebras and spin representation Spin structures Dirac operators Analytical properties of Dirac operators Eigenvalue estimates for the Dirac operator and twistor spinors Seiberg-Wittenβ¦ Expand

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.β¦ Expand