Clifford Algebras and Spinor Structures de Rafal Ablamowicz

Clifford Algebras and Spinor Structures

Rafal Ablamowicz

P. Lounesto

This volume is dedicated to the memory of Albert Crumeyrolle, who died on June 17, 1992. In organizing the volume we gave priority to: articles summarizing Crumeyrolle's own work in differential geometry, general relativity and spinors, articles which give the reader an idea of the depth and breadth of Crumeyrolle's research interests and influence in the field, articles of high scientific quality which would be of general interest. In each of the areas to which Crumeyrolle made significant contribution - Clifford and exterior algebras, Weyl and pure spinors, spin structures on manifolds, principle of triality, conformal geometry - there has been substantial progress. Our hope is that the volume conveys the originality of Crumeyrolle's own work, the continuing vitality of the field he influenced, and the enduring respect for, and tribute to, him and his accomplishments in the mathematical community. It isour pleasure to thank Peter Morgan, Artibano Micali, Joseph Grifone, Marie Crumeyrolle and Kluwer Academic Publishers for their help in preparingthis volume.

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Cuprins

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.