Albrecht Fröhlich

from Wikipedia, the free encyclopedia

Albrecht Fröhlich , called Ali Fröhlich, (born May 22, 1916 in Munich , † November 8, 2001 in Cambridge ) was a British mathematician who studied algebra and number theory.

life and work

Fröhlich (whose family came from the Black Forest and whose father was a cattle dealer) fled as a Jew with his parents from the National Socialists, first to Alsace in France and then to Haifa in Palestine , where his sister already lived. There he made a living as a railroad electrician. From 1945 he studied at the University of Bristol (despite the lack of high school diplomas thanks to the help of his older brother Herbert Fröhlich , a well-known physicist, at the University of Bristol since 1935), where he received his doctorate in 1951 under Hans Heilbronn ( On Some Topics in the Theory of Representation of Groups and Individual Class Field Theory ). He was then from 1950 to 1952 lecturer at the University of Leicester and at Keele University (University College of North Staffordshire, 1952-1955), before he was 1955 "Reader" and 1962 professor at King's College London . From 1969 he was director of the there Mathematics Faculty. In 1981 he retired there and was then at Robinson College, Cambridge University and Senior Research Fellow at Imperial College London . Among other things, he was visiting professor at the University of Bordeaux (1975, 1984) and in Heidelberg.

Fröhlich is considered the founder of a modern algebraic method (in the tradition of Emmy Noether , Helmut Hasse ) using algebraic number theory in Great Britain, where number theory was otherwise traditionally strongly attached to analytical methods. In 1965 he organized an influential conference on class field theory with Ian Cassels in Brighton , and the accompanying book is one of the standard works on algebraic number theory. In 1972 he succeeded in showing a surprising connection between the Galois group structure of the ring of whole numbers in an algebraic number field and analytic invariants, the Artin Root Numbers in the functional equation of the Artin L-functions. He is considered to be the founder of the arithmetic theory of the Galois modules.

In 1976 Fröhlich became a Fellow of the Royal Society. In 1976 he received the Senior Berwick Prize of the London Mathematical Society (LMS) and in 1992 their De Morgan Medal . He was an honorary doctor of the Universities of Bristol and Bordeaux and received the Alexander von Humboldt Prize in 1992. In 1974 he was an Invited Lecturer at the ICM (Galois module structure and Artin L functions). In 1982 he became a member of the Heidelberg Academy of Sciences .

In his honor, the LMS created the Fröhlich Prize , which will be awarded every two years from 2004 for extraordinarily innovative work in mathematics. The first award winner was Ian Grojnowski .

He had been married to doctor Ruth Brooks since 1950.

His PhD students include David Burns (University of London), Martin Taylor (University of Manchester) and Colin Bushnell .


  • as editor with John WS Cassels : Algebraic Number Theory. Proceedings of an Instructional Conference organized by the London Mathematical Society (a NATO Advanced Study Institute) with the Support of the International Mathematical Union. Academic Press, New York NY 1967, (therein, pp. 1-41, by Fröhlich Local Fields. ).
  • Formal Groups (= Lecture Notes in Mathematics . Vol. 74). Springer, Berlin et al. 1968.
  • as editor: Algebraic Number fields. (L-Functions and Galois Properties). Proceedings of a Symposium organized by the London Mathematical Society with the support of the Science Research Council and the Royal Society. Academic Press, London et al. 1977.
  • Galois module structure of algebraic integers (= results of mathematics and its border areas . Volume 3, Vol. 1). Springer, Berlin et al. 1983, ISBN 3-540-11920-5 .
  • Central extensions, Galois groups, and ideal class groups of number fields (= Contemporary Mathematics . 24). American Mathematical Society, Providence RI 1983, ISBN 0-8218-5022-9 .
  • with Colin J. Bushnell : Gauss sums and p-adic division algebras (= Lecture Notes in Mathematics. 987). Springer, Berlin et al. 1983, ISBN 3-540-12290-7 .
  • Classgroups and Hermitian modules (= Progress in Mathematics. 48). Birkhäuser, Boston MA et al. 1984, ISBN 0-8176-3182-8 .
  • with Martin J. Taylor : Algebraic number theory (= Cambridge Studies in Advanced Mathematics. 27). Cambridge University Press, Cambridge et al. 1991, ISBN 0-521-36664-X .


  • Bryan J. Birch , Martin J. Taylor: Albrecht Fröhlich. In: Biographical Memoirs of Fellows of the Royal Society of London. Vol. 51, 2005, pp. 150-168, JSTOR 30036889 .

Web links

Individual evidence

  1. Published in two parts: The representation of a finite group as a group of automorphisms on a finite Abelian group. In: Quarterly Journal of Mathematics. Serie 2, Vol. 1, No. 1, 1950, ISSN  0033-5606 , pp. 270-283, doi : 10.1093 / qmath / 1.1.270 and On the class group of relatively Abelian fields. In: Quarterly Journal of Mathematics. Series 2, Vol. 3, No. 1, 1952, pp. 98-106, doi : 10.1093 / qmath / 3.1.98 .
  2. ^ Albrecht Fröhlich: Artin-Root Numbers and Normal Integral Bases for Quaternion Fields. In: Inventiones Mathematicae . Vol. 17, 1972, pp. 143-166 .
  3. Martin J. Taylor: Obituary. In: Bulletin of the London Mathematical Society. Vol. 38, No. 2, 2006, pp. 329-350, doi : 10.1112 / S0024609306018443
  4. ^ Gabriele Dörflinger: Mathematics in the Heidelberg Academy of Sciences . 2014, p. 20.
  5. ^ Mathematics Genealogy Project