Gerhard Hochschild

Who was Gerhard Hochschild?

Gerhard Paul Hochschild was a German-born 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 introduced Hochschild cohomology, a cohomology theory for algebras, which classifies deformations of algebras. Hochschild & Nakayama introduced cohomology into class field theory.

Among his students were Andrzej Białynicki-Birula and James Ax.

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.