Pierre Gabriel

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Pierre Gabriel (also Peter Gabriel ; born August 1, 1933 in Bitsch ; † November 24, 2015 in St. Gallen , Switzerland ) was a French mathematician who studied algebra and homological algebra .

Life

Gabriel received his doctorate from the University of Paris in 1960 (Des categories abeliennes) . He was a professor at the Universities of Strasbourg-Metz, Bonn and Zurich.

Gabriel was also a student of Jean-Pierre Serre , who strongly influenced him in his field of work, and gave the first version of his Algèbre locale. Multiplicités from lectures at the Collège de France 1957/58.

In his dissertation (published in 1962 in the Bulletin de la Société Mathématique de France ), Gabriel made significant advances in the theory of Abelian categories , in particular the categories of quasi-coherent sheaves on schemes (including the Gabriel Rosenberg reconstruction theorem, also named after Alexander L. Rosenberg ). He worked for Alexander Grothendieck in SGA 1 and 3 (Seminar Géometrie Algébrique).

With Michel Zisman he developed a generalized localization theory in homotopy theory . With Michel Demazure he wrote a textbook on algebraic groups with an emphasis on the view of homological algebra. Later he dealt with representation theory of finite-dimensional associative algebras. In 1970 he showed that quivers of finite type (with a finite number of indecomposable representations) correspond to the Dynkin diagrams . With Raimundo Bautista, AV Roiter (1937–2006) and Leonardo Salmeron, he proved in 1983 the existence of multiplicative bases in representational algebras (published in Inventiones Mathematicae in 1985).

In 1986 he became a corresponding member of the Académie des sciences . In 1980/81 he was President of the Swiss Mathematical Society .

Klaus Bongartz , Bernhard Keller and Christine Riedtmann were among his doctoral students .

In 1986 he was invited speaker at the International Congress of Mathematicians in Berkeley (representation of finite-dimensional algebras) .

Gabriel also campaigned for the preservation of Franco-German bilingualism in his Alsace-Lorraine homeland.

literature

  • (with Michel Demazure ) Groupes Algèbriques. Volume 1. Masson, Paris 1970 (the subsequent volumes never appeared). English edition of chap. 1: Introduction to algebraic geometry and algebraic groups , North Holland 1980
  • (with Michel Zisman) Calculus of fractions and homotopy theory. Springer, Berlin 1967 ( results of mathematics and its border areas. Vol. 35).
  • (with Friedrich Ulmer) Locally presentable categories. Springer, Berlin 1971 ( Lecture notes in Mathematics. Vol. 221).
  • (with Walter Borho , Rudolf Rentschler ) Primary ideals in envelopes solvable Lie algebras. Description by path rooms , Springer Verlag 1973 (as Peter Gabriel)
  • (with AV Roiter and B. Keller) Representations of finite dimensional algebras , Springer Verlag 1997
  • (with R. Bautista, A. Roiter, L. Salmeron): Representation-finite algebras and multiplicative bases , Inventiones Mathematicae, Volume 81, 1985, pp. 217-285
  • Matrices, Geometry, Linear Algebra , Birkhäuser Verlag 1996, ISBN 978-3-0348-9873-7 , DOI: 10.1007 / 978-3-0348-9026-7 (translated into French, and supplemented, by G. Arnaudiès, J. –M. Arnaudiès, J.–D. Eiden and P. Gabriel, Éditions Cassini, Paris 2000)
  • The universal cover of a representation-finite algebra , in: Representations of Algebras, Lecture Notes in Mathematics 903, 1981, pp. 68-105
  • Auslandser-riding sequences in representation-finite algebras , in: Representation Theory I, Lecture Notes in Mathematics 831, Springer Verlag 1980, pp. 1–71

Web links

Individual evidence

  1. ↑ Décès de Pierre Gabriel militant du bilinguisme , Culture et bilinguisme de Lorraine; Retrieved December 3, 2015.
  2. ↑ ETHZ obituary: Peter Gabriel , Neue Zürcher Zeitung , December 3, 2015
  3. ↑ Pierre Gabriel in the Mathematics Genealogy Project (English)Template: MathGenealogyProject / Maintenance / id used
  4. ^ Gabriel-Rosenberg theorem , nLab
  5. ↑ Gabriel Indecomposable Representations. I , Manuscripta Mathematica, Volume 6, 1972, pp. 71-103
personal data
SURNAME Gabriel, Pierre
ALTERNATIVE NAMES Gabriel, Peter
BRIEF DESCRIPTION French mathematician
DATE OF BIRTH August 1, 1933
PLACE OF BIRTH Bitsch
DATE OF DEATH November 24, 2015
Place of death St. Gallen , Switzerland