Gerhard Hochschild
Encyclopedia
Gerhard Paul Hochschild was an American mathematician who worked on Lie group
s, algebraic group
s, 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
.
introduced Hochschild cohomology, a cohomology theory for algebras, which classifies deformations of algebras. 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
.
Lie group
In mathematics, a Lie group is a group which is also a differentiable manifold, with the property that the group operations are compatible with the smooth structure...
s, algebraic group
Algebraic group
In algebraic geometry, an algebraic group is a group that is an algebraic variety, such that the multiplication and inverse are given by regular functions on the variety...
s, homological algebra
Homological algebra
Homological algebra is the branch of mathematics which studies homology in a general algebraic setting. It is a relatively young discipline, whose origins can be traced to investigations in combinatorial topology and abstract algebra at the end of the 19th century, chiefly by Henri Poincaré and...
and algebraic number theory
Algebraic number theory
Algebraic number theory is a major branch of number theory which studies algebraic structures related to algebraic integers. This is generally accomplished by considering a ring of algebraic integers O in an algebraic number field K/Q, and studying their algebraic properties such as factorization,...
.
Hochschild wrote his thesis in 1941 at Princeton University
Princeton University
Princeton University is a private research university located in Princeton, New Jersey, United States. The school is one of the eight universities of the Ivy League, and is one of the nine Colonial Colleges founded before the American Revolution....
with Claude Chevalley
Claude Chevalley
Claude Chevalley was a French mathematician who made important contributions to number theory, algebraic geometry, class field theory, finite group theory, and the theory of algebraic groups...
on Semisimple Algebras and Generalized Derivations. In 1956/7 he was at the Institute for Advanced Study
Institute for Advanced Study
The Institute for Advanced Study, located in Princeton, New Jersey, United States, is an independent postgraduate center for theoretical research and intellectual inquiry. It was founded in 1930 by Abraham Flexner...
. He was professor at the University of Illinois at Urbana-Champaign
University of Illinois at Urbana-Champaign
The University of Illinois at Urbana–Champaign is a large public research-intensive university in the state of Illinois, United States. It is the flagship campus of the University of Illinois system...
and from the end of the 1950s at the University of California, Berkeley
University of California, Berkeley
The University of California, Berkeley , is a teaching and research university established in 1868 and located in Berkeley, California, USA...
.
introduced Hochschild cohomology, a cohomology theory for algebras, which classifies deformations of algebras. introduced cohomology into class field theory
Class field theory
In mathematics, class field theory is a major branch of algebraic number theory that studies abelian extensions of number fields.Most of the central results in this area were proved in the period between 1900 and 1950...
.
Among his students were Andrzej Białynicki-Birula and James Ax
James Ax
James Burton Ax was a mathematician who proved several results in algebra and number theory by using model theory. He shared the seventh Frank Nelson Cole Prize in Number Theory with Simon B. Kochen, which was awarded for a series of three joint papers on Diophantine problems.James Ax earned his...
.
In 1955 he was a Guggenheim Fellow. In 1979 he was elected to the National Academy of Sciences
United States National Academy of Sciences
The National Academy of Sciences is a corporation in the United States whose members serve pro bono as "advisers to the nation on science, engineering, and medicine." As a national academy, new members of the organization are elected annually by current members, based on their distinguished and...
, and in 1980 he was awarded the Leroy P. Steele Prize of the AMS
American Mathematical Society
The American Mathematical Society is an association of professional mathematicians dedicated to the interests of mathematical research and scholarship, which it does with various publications and conferences as well as annual monetary awards and prizes to mathematicians.The society is one of the...
.