Albert Crumeyrolle Explained
| Albert Crumeyrolle |
| Birth Date: | 10 December 1919 |
| Birth Place: | Curemonte, Corrèze, France |
| Death Date: | [1] |
| Death Place: | Toulouse, France |
| Nationality: | French |
| Fields: | Mathematics |
| Academic Advisors: | André Lichnerowicz |
| Known For: | major contributions to the study of Clifford algebras, in particular spinor structures and symplectic Clifford algebra |
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.
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]
[12]
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,
- 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,, p. 83–96
Notes and References
- 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,, Preface, p. viii
- http://www.gravityresearchfoundation.org/pdf/awarded/1975/crumetrolle.pdf Albert J. Crumeyrolle
- Artibano Micali: Albert Crumeyrolle: la démarche algébrique d'un géomètre. In: Pertti Lounesto, Rafał Abłamowicz (ed.): Clifford Algebras and Spinor Structures: A Special Volume Dedicated to the Memory of Albert Crumeyrolle (1919--1992), Springer Netherlands, 1995,, p. ix–xiv (in French language)
- Zbigniew Oziewicz, Bernard Jancewicz, Andrzej Borowiec (eds.): Spinors, Twistors and Clifford Algebras and Quantum Deformations: Proceedings of the II Max Born Symposium Held Near Wroclaw, Poland, September 1992 (Fundamental Theories of Physics), Springer, 1993, p. xv
- Publication by Nouazé and Revoy, cited by: Jacques Helmstetter: Lipschitz' methods of 1886 applied to symplectic Clifford algebras. In: Pertti Lounesto, Rafał Abłamowicz (ed.): Clifford Algebras: Applications to Mathematics, Physics, and Engineering, Birkhäuser, 2004,, pp. 323–334, therein p. 332
- Jacques Helmstetter: Lipschitz' methods of 1886 applied to symplectic Clifford algebras. In: Pertti Lounesto, Rafał Abłamowicz (ed.): Clifford Algebras: Applications to Mathematics, Physics, and Engineering, Birkhäuser, 2004,, pp. 323–334, therein p. 333
- Book: Orthogonal and symplectic Clifford algebras, spinor structures. 1990.
- Book: Crumeyrolle (1919-1992), Albert. Algèbres de Clifford et spineurs. March 4, 1974. data.bnf.fr.
- Book: Crumeyrolle (1919-1992), Albert. Bases géométriques de la topologie algébrique. March 4, 1970. data.bnf.fr.
- Book: Crumeyrolle (1919-1992), Albert. Compléments d'algèbre moderne, à l'usage des étudiants de 2e année du 1er cycle des facultés des sciences (MP 2) et des classes de mathématiques spéciales. March 4, 1969. data.bnf.fr.
- Web site: Notions fondamentales d'algèbre moderne (1er niveau), à l'usage des étudiants du 1er cycle des facultés des sciences et des classes préparatoires aux grandes écoles. Albert. Crumeyrolle (1919-1992). March 4, 1967. data.bnf.fr.
- Web site: Albert Crumeyrolle (1919-1992). data.bnf.fr.
