Gerhard Hochschild

Gerhard Paul Hochschild ( born April 29, 1915 in Berlin, † July 8th, 2010 in El Cerrito, California ) was an American mathematician who worked on algebra.

Hochschild was born into a Jewish family in Berlin visited the school and was sent in 1933 by his father, a patent attorney, with his brother due to the assumption of power by the National Socialists to Cape Town to safety. There he was forced to earn his own living as a photographer 's assistant ( the photograph was also later his hobby ). From 1934 he studied mathematics at the University of Cape Town with a Bachelor 's degree in physics and mathematics in 1936 and the Master degree in Mathematics, 1937. It was 1941, at Princeton University, where he studied with a recommendation of his teacher in South Africa Stanley Skewes since 1938 Claude Chevalley doctorate (Semi Simple Algebras and Generalized Derivations ). He was the candidate Chevalleys in Princeton, which gave him an insight into early Bourbaki manuscripts. From Chevalley he took over at that time also a passion for the game of Go. Among his teachers at Princeton included, in addition Chevalley Luther P. Eisenhart, John von Neumann, Salomon Bochner and Paul Halmos. After his graduation, he served in the U.S. Army as a mathematician in the calculation of ballistic tables in the Aberdeen Proving Ground under Oswald Veblen. After the war he was first instructor at Princeton, 1946-1948 Benjamin Peirce Instructor at Harvard University, from 1948 assistant professor and in 1952 professor at the University of Illinois at Urbana- Champaign. 1951/52, he was a visiting professor at Yale University, 1955/56, at the University of California, Berkeley, and 1956/7 he was at the Institute for Advanced Study. 1951 to 1954 he participated in the Bourbaki congresses as a visitor. From 1958 he was professor at the University of Berkeley, where he held emeritus in 1982, but until 1985 lectures.

Hochschild worked on Lie groups, algebraic groups and homological algebra. The eponymous concept of Hochschild homology defines a homology of algebras. There is also a Hochschild cohomology which classifies the deformation of algebras.

He led cohomology in the class field theory one ( after he had applied already cohomological methods in the theory of Lie groups ), first in the local theory and 1952, Tadashi Nakayama in the global theory, then what seminar in Princeton was expanded in known Artin - Tate.

The set of Hochschild - Kostant -Rosenberg ( HKR ), who struck a compound of the Hochschild homology of an algebra to differential forms later played a major role in non-commutative geometry of Alain Connes.

His doctoral include Andrzej Bialynicki - Birula, James Ax.

In 1955 he was Guggenheim Fellow. In 1980 he received the Leroy P. Steele Prize of the American Mathematical Society. From 1979 he was a member of the National Academy of Sciences and was a member of the American Academy of Arts and Sciences.

He was married to the deceased since 1950 2005 mathematician Ruth Heinsheimer ( a student of Reinhold Baer), with whom he had a son and a daughter.

Writings

  • The structure of Lie groups, Holden -Day, San Francisco 1965
  • Introduction to affine algebraic groups, Holden -Day, San Francisco 1971
  • Basic theory of algebraic groups and Lie algebras. Springer, Graduate Texts in Mathematics, 1981.
  • Perspectives of elementary mathematics. Springer 1983.
  • A second introduction to analytic geometry, Holden - Day 1968
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