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Albert Crumeyrolle

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Albert Crumeyrolle
Born10 December 1919
Curemonte, Corrèze, France
Died17 June 1992 (1992-06-18) (aged 72)[1]
Toulouse, France
NationalityFrench
Known formajor contributions to the study of Clifford algebras, in particular spinor structures and symplectic Clifford algebra
Scientific career
FieldsMathematics
Academic advisorsAndré Lichnerowicz

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

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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

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Books

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  • 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

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  • 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

References

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  1. ^ 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, Preface, p. viii
  2. ^ Jump up to: a b Albert J. Crumeyrolle[permanent dead link], www.gravityresearchfoundation.org
  3. ^ Jump up to: a b 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, ISBN 0-7923-3366-7, p. ix–xiv (in French language)
  4. ^ 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
  5. ^ 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, ISBN 978-0-8176-3525-1, pp. 323–334, therein p. 332
  6. ^ 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, ISBN 978-0-8176-3525-1, pp. 323–334, therein p. 333
  7. ^ Orthogonal and symplectic Clifford algebras, spinor structures. 1990.
  8. ^ Crumeyrolle (1919-1992), Albert (March 4, 1974). Algèbres de Clifford et spineurs – via data.bnf.fr.{{cite book}}: CS1 maint: numeric names: authors list (link)
  9. ^ Crumeyrolle (1919-1992), Albert (March 4, 1970). Bases géométriques de la topologie algébrique – via data.bnf.fr.{{cite book}}: CS1 maint: numeric names: authors list (link)
  10. ^ Crumeyrolle (1919-1992), Albert (March 4, 1969). 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 – via data.bnf.fr.{{cite book}}: CS1 maint: numeric names: authors list (link)
  11. ^ Crumeyrolle (1919-1992), Albert (March 4, 1967). "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" – via data.bnf.fr.{{cite web}}: CS1 maint: numeric names: authors list (link)
  12. ^ "Albert Crumeyrolle (1919-1992)". data.bnf.fr.
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