A binary encoding of spinors and applications

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 𝔰𝔭𝔦𝔶 (8), 𝔰𝔭𝔦𝔶 (7) and 𝔤2, etc.

Keywords

• spin representation
• clifford algebras
• spinor representation
• octonions
• triality
• 15a66
• 15a69
• 53c27
• 17b10
• 17b25
• 20g41