Albert J. Crumeyrolle (1919–1992) was a

French French (french: français(e), link=no) may refer to: * Something of, from, or related to France ** French language, which originated in France, and its various dialects and accents ** French people, a nation and ethnic group identified with France ...

mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, mathematical structure, structure, space, Mathematica ...

and

professor Professor (commonly abbreviated as Prof.) is an academic rank at universities and other post-secondary education and research institutions in most countries. Literally, ''professor'' derives from Latin as a "person who professes". Professor ...

of mathematics at the

Paul Sabatier University Paul Sabatier University (''Université Paul Sabatier'', UPS, also known as Toulouse III) is a French public university, in the Academy of Toulouse. It is one of the several successor universities of the University of Toulouse. Toulouse III was ...

, known for his contributions to

spinor In geometry and physics, spinors are elements of a complex vector space that can be associated with Euclidean space. Like geometric vectors and more general tensors, spinors transform linearly when the Euclidean space is subjected to a sligh ...

structures and

Clifford algebra In mathematics, a Clifford algebra is an algebra generated by a vector space with a quadratic form, and is a unital associative algebra. As -algebras, they generalize the real numbers, complex numbers, quaternions and several other hyperc ...

Work

Crumeyrolle was a student of

André Lichnerowicz André Lichnerowicz (January 21, 1915, Bourbon-l'Archambault – December 11, 1998, Paris) was a noted French differential geometer and mathematical physicist of Polish descent. He is considered the founder of modern Poisson geometry. Biography H ...

under whose supervision he completed a thesis in 1961.Albert J. Crumeyrolle
www.gravityresearchfoundation.org His first important paper after completing his doctorate addressed spinor structures using methods of Clifford algebras developed by

Claude Chevalley Claude Chevalley (; 11 February 1909 – 28 June 1984) was a French mathematician who made important contributions to number theory, algebraic geometry, class field theory, finite group theory and the theory of algebraic groups. He was a foun ...

.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) 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 In abstract algebra, the Weyl algebra is the ring of differential operators with polynomial coefficients (in one variable), namely expressions of the form : f_m(X) \partial_X^m + f_(X) \partial_X^ + \cdots + f_1(X) \partial_X + f_0(X). More preci ...

and the symplectic

. 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. His work on symplectic Clifford algebras however came under serious critique on mathematical grounds. 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 Dmitri Ivanovich Mendeleev (sometimes transliterated as Mendeleyev or Mendeleef) ( ; russian: links=no, Дмитрий Иванович Менделеев, tr. , ; 8 February O.S. 27 January">Old_Style_and_New_Style_dates.html" ;"title="no ...

has played for the

periodic table The periodic table, also known as the periodic table of the (chemical) elements, is a rows and columns arrangement of the chemical elements. It is widely used in chemistry, physics, and other sciences, and is generally seen as an icon of ...

of elements. Crumeyrolle taught in Iran in 1966, in several Europe countries and, in 1973, at Stanford University summer school.

Publications

Books

* ''Orthogonal and symplectic Clifford algebras: Spinor Structures'', 1990 * Albert Crumeyrolle & J. Grifone: ''Symplectic geometry'', Pitman Advanced Publishing Program, 1983 * ''Algèbres de Clifford et spineurs'', 1974 * ''Bases géométriques de la topologie algébrique'', 1970 * ''Compléments d'algèbre moderne'', 1969 * ''Notions fondamentales d'algèbre moderne'', 1967

References

{{DEFAULTSORT:Crumeyrolle, Albert 1919 births 1992 deaths 20th-century French mathematicians

Work

Publications

Books

Further reading

References