Albert Crumeyrolle
French mathematician (1919–1992)
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Albert J. Crumeyrolle (1919–1992) was a French mathematician and professor of mathematics at the Paul Sabatier University, known for his contributions to spinor structures and Clifford algebra.
Albert Crumeyrolle | |
|---|---|
| Born | 10 December 1919 Curemonte, Corrèze, France |
| Died | 17 June 1992 (aged 72)[1] Toulouse, France |
| Known for | major contributions to the study of Clifford algebras, in particular spinor structures and symplectic Clifford algebra |
| Scientific career | |
| Fields | Mathematics |
Academic advisors | André Lichnerowicz |
Work
Crumeyrolle was a student of André Lichnerowicz under whose supervision he completed a thesis in 1961.[2]
His first important paper after completing his doctorate addressed spinor structures using methods of Clifford algebras developed by Claude Chevalley.[3]
Crumeyrolle is known for his major contributions to theories of Clifford algebras and spinor structures. In 1975 he laid the foundations for symplectic Clifford algebra and the symplectic spinor.[4] An earlier publication by two other authors, Nouazé and Revoy, had appeared three years before in which Weyl algebras were treated from a Cliffordian point of view. Crumeyrolle however drew more attention to the topic, and, as emphasized by Jacques Helmstetter, he contributed original ideas of his own.[5] His work on symplectic Clifford algebras however came under serious critique on mathematical grounds.[6]
The mathematician Artibano Micali recalled Crumeyrolle stating that periodicity of Clifford algebras should play a similar role for elementary particle physics as the periodic classification of elements by Dmitri Mendeleev has played for the periodic table of elements.[3]
Crumeyrolle taught in Iran in 1966, in several Europe countries and, in 1973, at Stanford University summer school.[2]
Publications
Books
- Orthogonal and symplectic Clifford algebras: Spinor Structures, 1990 [7]
- Albert Crumeyrolle & J. Grifone: Symplectic geometry, Pitman Advanced Publishing Program, 1983
- Algèbres de Clifford et spineurs, 1974 [8]
- Bases géométriques de la topologie algébrique, 1970 [9]
- Compléments d'algèbre moderne, 1969 [10]
- Notions fondamentales d'algèbre moderne, 1967 [11]
Further reading
- Rafał Abłamowicz, Pertti Lounesto (eds.): Clifford algebras and spinor structures: a special volume dedicated to the memory of Albert Crumeyrolle (1919–1992), Kluwer Academic Publishers, 1995, ISBN 0-7923-3366-7
- Z. Ozievicz, Cz. Sitarczyk: Parallel treatment of Riemannian and symplectic Clifford algebras. In: A. Micali, R. Boudet, J. Helmstetter (eds.): Clifford Algebras and their Applications in Mathematical Physics: Workshop Proceedings: 2nd (Fundamental Theories of Physics), Kluwer Academic Publishers, 1992, ISBN 978-0-7923-1623-7, p. 83–96