Willem Titus van Est

Willem Titus van Est (born September 12, 1921 in Batavia ; † July 30, 2002 in Leiderdorp ) was a Dutch mathematician who mainly dealt with Lie groups and Lie algebras .

Life

He went to school in Batavia, where his father was a police officer, and came to the Netherlands in 1938 to study mathematics and science at the University of Amsterdam. His teachers included Luitzen Egbertus Jan Brouwer , Arend Heyting and Hans Freudenthal . After the candidate exam in 1942, studies were interrupted by the Second World War. In 1948 he made his doctoral examination. Van Est received his doctorate in 1950 from Hans Freudenthal at the University of Utrecht (A Generalization of a Theorem of J. Nielsen Concerning Hyperbolic Groups). He followed Freudenthal to Utrecht as an assistant in 1947, but was then also a high school teacher in Alkmaarto support his family as a newlywed. In 1953 he became a lecturer and in 1955 an associate professor in Utrecht. In 1953/54 he was at Princeton University at the invitation of Ralph Fox . From 1956 he was a professor in Leiden and from 1972 at the University of Amsterdam. In 1986 he retired.

In his dissertation, he generalized Jakob Nielsen's theorem that a non-commutative group of hyperbolic isometries of the hyperbolic plane is necessarily discrete to the isometries of symmetrical spaces of non-compact type . He used properties of the associated Lie algebras . His dissertation showed a thorough knowledge of the work of Élie Cartan , which van Est also used in later work.

He is known for his results on the cohomology of Lie groups (isomorphism by van Est and theorem of van Est from 1953). At that time he used new methods of homological algebra and spectral sequences , with which he formulated his Van Est isomorphism more elegantly (the Van Est spectral sequence is named after him). Later he dealt with the integrability of Lie algebras. With Th. J. Korthagen he discovered that Lie's third theorem , that finitely dimensional Lie algebras can be integrated into Lie groups , does not apply to certain infinitely dimensional Lie algebras ( Banach Lie algebras ). This led him to investigate infinitely dimensional Lie algebras with application to scrolls . In search of more general manifolds to which the integration of Banach-Lie algebras leads, he introduced the term S-Atlas (S after the Japanese mathematician Ichirō Satake ) and in this context proved classical results of the theory of scrolls.

In 1973 he became a member of the Royal Netherlands Academy of Sciences. For a long time he was chairman of their natural science section. He was also active in the Centrum Wiskunde & Informatica and was on its board of trustees for many years. In 1987 he received an honorary doctorate from the University of Toulouse .

His hobby was the Spanish language and literature.

His PhD students include Antonius van de Ven and Frans Oort .

Fonts (selection)

• Dense imbeddings of Lie groups. Nederl. Akad. Wetensch. Proc. Ser. A. 54 = Indagationes Math. 13, (1951), 321-328.
• Group cohomology and Lie algebra cohomology in Lie groups. I, II. Nederl. Akad. Wetensch. Proc. Ser. A. 56 = Indagationes Math. 15, (1953), 484-492, 493-504.
• On the algebraic cohomology concepts in Lie groups. I, II. Nederl. Akad. Wetensch. Proc. Ser. A. 58 = Indag. Math. 17, (1955), 225-233, 286-294.
• with Korthagen: Non-enlargible Lie algebras. Nederl. Akad. Wetensch. Proc. Ser. A 67 = Indag. Math. 26: 15-31 (1964).
• Report on the S-Atlas. Transversal structure of foliations (Toulouse, 1982). Astérisque No. 116: 235-292 (1984).

literature

• I. Moerdijk, JP Murre: In memoriam Willem Titus van Est. Nieuw archief voor Wiskunde, 5/4, 2003, 281–283

Web links

• Het Biografisch Portaal van Nederland , accessed on February 12, 2015
• Page at the KNAW with obituaries from Moerdijk and Murre

Individual evidence

1. ↑ Willem Titus van Est in the Mathematics Genealogy Project (English)