Clifford Algebras and Spinor Structures

Table of Contents/Table des Matières.- Historical Survey.- Some Clifford algebra history.- Clifford Algebras.- Tensors and Clifford algebra.- Sur les algèbres de Clifford III.- Finite geometry, Dirac groups and the table of real Clifford algebras.- Clifford algebra techniques in linear algebra.- Crumeyrolle/Chevalley, Weyl, Pure and Majorana Spinors.- Construction of spinors via Witt decomposition and primitive idempotents: a review.- Crumeyrolle-Chevalley-Riesz spinors and covariance.- Twistors as geometric objects in spacetime.- Crumeyrolle’s bivectors and spinors.- On the relationships between the Dirac spinors and Clifford subalgebra Cl1,3+.- Spinor fields and superfields as equivalence classes of exterior algebra fields.- Chevalley-Crumeyrolle spinors in McKane-Parisi-Sourlas theorem.- Spinors from a differential geometric point of view.- Dirac Operator, Maxwell’s Equations, and Conformal Covariance.- Eigenvalues of the Dirac operator, twistors and Killing spinors on Riemannian manifolds.- Dirac’s field operator ?.- Biquaternionic formulation of Maxwell’s equations and their solutions.- The massless Dirac equation, Maxwell’s equation, and the application of Clifford algebras.- The conformal covariance of Huygens’ principle-type integral formulae in Clifford analysis.- Clifford Analysis, Boundary Value Problems, Hermite Interpolants, and Padé Approximants.- Cliffor-valued functions in Cl3.- Clifford analysis and elliptic boundary value problems.- A complete boundary collocation system.- On the algebraic foundations of the vector ?-algorithm.- Clifford Algebras and Generalizations.- Classical spinor structures on quantum spaces.- A unified metric.- Quantum braided Clifford algebras.- Clifford algebra for Hecke braid.