Gerhard Hochschild

Gerhard Paul Hochschild (April 29, 1915, Berlin – July 8, 2010 El Cerrito, California) was an American mathematician who worked on Lie groups, algebraic groups, homological algebra and algebraic number theory.

Hochschild wrote his thesis in 1941 at Princeton University with Claude Chevalley on Semisimple Algebras and Generalized Derivations. In 1956/7 he was at the Institute for Advanced Study. He was professor at the University of Illinois at Urbana-Champaign and from the end of the 1950s at the University of California, Berkeley.

Hochschild (1945) introduced Hochschild cohomology, a cohomology theory for algebras, which classifies deformations of algebras. Hochschild & Nakayama (1952) introduced cohomology into class field theory.

In 1955 he was a Guggenheim Fellow. In 1979 he was elected to the National Academy of Sciences, and in 1980 he was awarded the Leroy P. Steele Prize of the AMS.

Publications

Hochschild, G. (1945), "On the cohomology groups of an associative algebra", Annals of Mathematics. Second Series 46: 58–67, ISSN 0003-486X, JSTOR 1969145, MR 0011076
Hochschild, G.; Nakayama, Tadasi (1952), "Cohomology in class field theory", Annals of Mathematics. Second Series 55: 348–366, ISSN 0003-486X, JSTOR 1969783, MR 0047699
Hochschild, G. (1965), The structure of Lie groups, San Francisco, Calif.: Holden–Day Inc., MR 0207883
Hochschild, G. (1971), Introduction to affine algebraic groups, San Francisco, Calif.: Holden–Day Inc., MR 0277535
Hochschild, Gerhard Paul (1981), Basic theory of algebraic groups and Lie algebras, Graduate Texts in Mathematics, 75, Berlin, New York: Springer-Verlag, ISBN 978-0-387-90541-9, MR 620024
Hochschild, Gerhard Paul (1983), Perspectives of elementary mathematics, Berlin, New York: Springer-Verlag, ISBN 978-0-387-90848-9, MR 710303