Crumeyrolle was a student ofAndré 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 byClaude Chevalley.[3]
Crumeyrolle is known for his major contributions to theories of Clifford algebras and spinor structures. In 1975 he laid the foundations forsymplectic Clifford algebra and the symplecticspinor.[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 byDmitri Mendeleev has played for theperiodic table of elements.[3]
Crumeyrolle taught in Iran in 1966, in several Europe countries and, in 1973, atStanford University summer school.[2]
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,ISBN0-7923-3366-7
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,ISBN978-0-7923-1623-7,p. 83–96
^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,ISBN0-7923-3366-7, Preface, p. viii
^abArtibano 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,ISBN0-7923-3366-7, 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,ISBN978-0-8176-3525-1, pp. 323–334, thereinp. 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,ISBN978-0-8176-3525-1, pp. 323–334, thereinp. 333
