Clifford Algebras and Spinor Structures

1. Front Matter

   Pages i-xx

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2. Historical Survey

   1. Front Matter

      Pages 1-1

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   2. Some Clifford Algebra History

      • Adel Diek, R. Kantowski

      Pages 3-12

3. Clifford Algebras

   1. Front Matter

      Pages 13-13

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   2. Tensors and Clifford Algebra

      • Alphonse Charlier, Marie-France Charlier, André Roux

      Pages 15-38

   3. Sur Les Algèbres de Clifford III

      • Artibano Micali

      Pages 39-57

   4. Finite Geometry, Dirac Groups and the Table of Real Clifford Algebras

      • R. Shaw

      Pages 59-99

   5. Clifford Algebra Techniques in Linear Algebra

      • Garret Sobczyk

      Pages 101-109

4. Crumeyrolle/Chevalley, Weyl, Pure and Majorana Spinors

   1. Front Matter

      Pages 111-111

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   2. Construction of Spinors via Witt Decomposition and Primitive Idempotents: A Review

      • Rafał Abłamowicz

      Pages 113-123

   3. Crumeyrolle-Chevalley-Riesz Spinors and Covariance

      • George Jones, W. E. Baylis

      Pages 125-132

   4. Twistors as Geometric Objects in Spacetime

      • Jaime Keller

      Pages 133-135

   5. Crumeyrolle’s Bivectors and Spinors

      • Pertti Lounesto

      Pages 137-166

   6. On the Relationships between the Dirac Spinors and Clifford Subalgebra Cl ⁺_1,3

      • Franco Piazzese

      Pages 167-176

   7. Spinor Fields and Superfields as Equivalence Classes of Exterior Algebra Fields

      • Waldyr A. Rodrigues Jr., Quintino A. G. De Souza, Jayme Vaz Jr.

      Pages 177-198

   8. Chevalley-Crumeyrolle Spinors in McKane-Parisi-Sourlas Theorem

      • Suemi Rodríguez-Romo

      Pages 199-204

   9. Spinors from a Differential Geometric Point of View

      • M. Rosenbaum, C. P. Luehr, H. Harleston

      Pages 205-240

5. Dirac Operator, Maxwell’s Equations, and Conformal Covariance

   1. Front Matter

      Pages 241-241

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   2. Eigenvalues of the Dirac Operator, Twistors and Killing Spinors on Riemannian Manifolds

      • Helga Baum, Thomas Friedrich

      Pages 243-256

   3. Dirac’s Field Operator Ψ

      • H. T. Cho, Adel Diek, R. Kantowski

      Pages 257-263

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.

• Dirac equation
• Maxwell's equation
• algebra
• clifford algebra
• complex analysis
• differential geometry
• eigenvalue
• field
• geometry
• linear algebra
• manifold
• mechanics
• quantum mechanics

• Gannon University, Erie, USA

  Rafał Ablamowicz

• Helsinki University of Technology, Espoo, Finland

  Pertti Lounesto

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