Jacques Tits

Jacques Tits ( born August 12, 1930 in Uccle / Ukkel ) is a Belgian- French mathematician who works mainly in the field of group theory and algebraic geometry. He is an honorary professor at the Collège de France in Paris.

Life

Tits is a native Belgians and went in Uccle / Ukkel in Brussels to school. He studied at the French-speaking Free University of Brussels ( Université Libre de Bruxelles), where he. Received his doctorate in 1950 with Paul Libois ( generalization of the groupes sur la notion de projectifs Bases transitivité ) 1956 to 1962 he was an assistant and from 1962 to 1964 professor at the Université Libre de Bruxelles, then to 1974 at the University of Bonn, before he became a professor at the Collège de France (emeritus 2000). After his retirement he was the first Vallée- Poussin Visiting Professor at the Université catholique de Louvain in Louvain- la -Neuve.

He is married to the historian Marie -Jeanne Dieuaide since 1956. Tits is a French citizen.

1980 to 1999 he was editor of the Publications Mathematiques de l' IHES.

Work

In the 1960s, Tits worked a lot with Armand Borel on algebraic groups. He is the inventor of the theory of building ( buildings ), combinatorial structures that operate on these groups, the Tits initially examined to investigate generalizations of simple Lie groups over arbitrary fields. Building can not only be on real and complex bodies define, but also p- adic numbers or finite fields and thus have applications in algebraic geometry and number theory. Tits classified irreducible spherical building is connected with a rank greater than or equal to 3 with the theory of building the theory of pairs of a group, ( Borel subgroup ) and are subsets of the produce. Moreover, the intersection of (the Cartan subgroup ) a normal subgroup in, and the factor group ( the Weyl group ) is generated by elements of order 2 (ie, " reflections "). The whole is generalized from the theory of Lie algebras and allows simplified and general valid evidence. With ( B, N) pairs can also construct buildings that are neither affine nor are spherical, but of infinite dimensional Lie groups result ( Kac -Moody algebras ).

" Tits alternative ": Each subgroup finitely generated linear group either has a solvable subgroup of finite index or a free subgroup of rank 2

He also worked on finite simple groups, for example, about the "monster ". A finite simple group, the Tits group, is named after him. The Tits group is the commutator subgroup of the twisted Chevalley group of type over the finite field GF (2).

Tits classified the polar space of finite rank greater or equal to three and more generally the so-called spherical building of rank greater than or equal three. Further work is dedicated to groups defined by geometries, for example - Moufang octagons, projective planes with the Suzuki groups and automorphisms of generalized -gone, automorphism groups of " trees ", quadratic forms, Buekenhout - Tits geometry and Clifford algebras.

Honors and Awards

In 1976 he received the Grand Prize of the French Academy of Sciences, whose corresponding member he which he belongs since 1977 and since 1979. 1962 in Stockholm ( Groupes et simple geometries Associees ) and in 1974 in Vancouver (On Buildings and Their Application), he gave a plenary lecture at the ICM. In 1970 he was invited speaker at the ICM in Nice ( Homomorphismes et automorphismes " abstrait " de groupes et algebriques Arithmétiques ). He received the 1993 Wolf Prize and is a member of the Order Pour le Mérite for Sciences and Arts since 1995. In 1996 he received the Georg Cantor Medal of the German Mathematical Society and in March 2008, together with John Griggs Thompson award the Abel Prize for outstanding contributions to algebra.

He is a member of the German Academy of Sciences Leopoldina ( since 1977), the Academia Europaea, the Belgian and Dutch Academy of Sciences, the American Academy of Arts and Sciences, the National Academy of Sciences, the London Mathematical Society. He is a Knight of the Legion of Honour (1995 ) and honorary doctorates from the universities of Utrecht, Ghent, Bonn and lions. In 2009 he was awarded the Federal Cross of Merit.

Writings

  • Lie groups and algebras. Springer college text 1983, ISBN 978-3-540-12547-1, doi: 10.1007/978-3-642-69189-8.
  • Tables to the simple Lie groups and their representations. Springer 1967, 53 pages.
  • Lectures on algebraic groups. 1967 ( Yale ).
  • Buildings of spherical type and finite pairs. Springer Lectures Notes in Mathematics 1974.
  • With Francois Bruhat: Groups reductifs sur une corps locaux. 1-3, Publ.Math.IHES 1972, 1984, J.Fac.Sci.Univ.Tokio 1987.
  • A local approach to buildings. In: The geometric vein. Coxeter Festschrift, 1981.
  • Symmetry in Michael Atiyah et al Miscellanea Mathematica, Springer Verlag 1991
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