Clifford geometric algebra: Real and complex spinor data tables

TL;DR

This paper presents comprehensive tables of algebraic spinors and matrix representations for various Clifford algebras with real and complex coefficients, facilitating advanced algebraic and geometric computations.

Contribution

It provides detailed, previously unpublished data tables of Clifford algebra spinors and their matrix representations using Mathematica, expanding on earlier work from 1998.

Findings

Tables include idempotents, ideals, and spinor bases.

Matrix representations of basis vectors are provided.

Norms of spinors are computed and tabulated.

Abstract

The modern algebra concepts are used to construct tables of algebraic spinors related to Clifford algebra multivectors with real and complex coefficients. The following data computed by Mathematica are presented in form of tables for individual Clifford geometric algebras: 1. Initial idempotent; 2. Two-sided ideal; 3. Left ideal basis (otherwise projector, or spinor basis); 4. Matrix representations (reps) for basis vectors in Clifford algebras in spinor basis; 5. General spinor; 6. Spinor in matrix form; 7. Squared hermitian norm of the spinor. Earlier in 1998, only the first four items computed by Maple were published by R. Ablamowicz.