Michel Enock-Levi (1 June 1947 – June 2025) was a French mathematician and a , credited with the early development of Pontryagin-style dualities for non-commutative topological groups.

Scientific contributions

Enock is known for the 1992 book co-authored with Jean-Marie Schwartz on the subject of Kac algebras, (not to be confused with Kac-Moody algebras). According to the French mathematician

Alain Connes Alain Connes (; born 1 April 1947) is a French mathematician, known for his contributions to the study of operator algebras and noncommutative geometry. He was a professor at the , , Ohio State University and Vanderbilt University. He was awar ...

, the book develops the general theory to characterize

quantum groups In mathematics and theoretical physics, the term quantum group denotes one of a few different kinds of noncommutative algebras with additional structure. These include Drinfeld–Jimbo type quantum groups (which are quasitriangular Hopf algebra ...

among

Hopf algebras In mathematics, a Hopf algebra, named after Heinz Hopf, is a structure that is simultaneously a (unital algebra, unital associative) Associative algebra, algebra and a (counital coassociative) coalgebra, with these structures' compatibility making ...

, similar to the characterization of

Lie groups In mathematics, a Lie group (pronounced ) is a group that is also a differentiable manifold, such that group multiplication and taking inverses are both differentiable. A manifold is a space that locally resembles Euclidean space, whereas ...

among

locally compact group In mathematics, a locally compact group is a topological group ''G'' for which the underlying topology is locally compact and Hausdorff. Locally compact groups are important because many examples of groups that arise throughout mathematics are lo ...

s, "with emphasis on the analytical aspects of the subject instead of the purely algebraic ones". Further, Connes writes: Specifically, Enock co-developed a general

Pontryagin duality In mathematics, Pontryagin duality is a duality between locally compact abelian groups that allows generalizing Fourier transform to all such groups, which include the circle group (the multiplicative group of complex numbers of modulus one), ...

theory for all

Scientific career

Enock completed his postgraduate thesis (1971) and state thesis (1976) at

Pierre and Marie Curie University Pierre and Marie Curie University ( , UPMC), also known as Paris VI, was a public research university in Paris, France, from 1971 to 2017. The university was located on the Jussieu Campus in the Latin Quarter of the 5th arrondissement of Paris, ...

. In 1971, he became an assistant professor at the University of Paris 13 (

Sorbonne Paris North University Sorbonne Paris North University () is a public university based in Paris, France. It is one of the thirteen universities that succeeded the University of Paris in 1968. It is a multidisciplinary university located in north of Paris, in the munici ...

). From 1978, he was a Researcher at the

French National Centre for Scientific Research The French National Centre for Scientific Research (, , CNRS) is the French state research organisation and is the largest fundamental science agency in Europe. In 2016, it employed 31,637 staff, including 11,137 tenured researchers, 13,415 engi ...

(CNRS). He received accreditation to direct research at

Paris Diderot University Paris Diderot University, also known as Paris 7 (), was a French university located in Paris, France. It was one of the inheritors of the historic University of Paris, which was split into 13 universities in 1970. Paris Diderot merged with Pari ...

in 1985. Enock became a Director of Research at CNRS in 2000 and a First class Research Director in 2011. From 2012, he was Emeritus Research Director at CNRS.

References

External links

* Michel Enock'
mathematics publications
at

zbMATH Open zbMATH Open, formerly Zentralblatt MATH, is a major reviewing service providing reviews and abstracts for articles in pure and applied mathematics, produced by the Berlin office of FIZ Karlsruhe – Leibniz Institute for Information Infrastru ...

Preprints by Michel Enock
on

arXiv arXiv (pronounced as "archive"—the X represents the Chi (letter), Greek letter chi ⟨χ⟩) is an open-access repository of electronic preprints and postprints (known as e-prints) approved for posting after moderation, but not Scholarly pee ...

{{DEFAULTSORT:Enock, Michel 1947 births 2025 deaths 20th-century French mathematicians 21st-century French mathematicians Pierre and Marie Curie University alumni French National Centre for Scientific Research scientists Academic staff of Paris-Sorbonne University Academic staff of Paris Diderot University Place of birth missing Research directors of the French National Centre for Scientific Research