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Gerhard Paul Hochschild (April 29, 1915 in Berlin – July 8, 2010 in El Cerrito, California) 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 (1945) introduced Hochschild cohomology, a cohomology theory for algebras, which classifies deformations of algebras. Hochschild & Nakayama (1952) introduced cohomology into class field theory. Along with Bertram Kostant and Alex F. T. W. Rosenberg, the Hochschild–Kostant–Rosenberg theorem is named after him.
- 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
- Porter, Tim (April 8, 2014), "Hochschild-Kostant-Rosenberg theorem", nLab.
- Moore, Calvin C.; Ribet, Kenneth A.; Wolf, Joseph A. (2011), IN MEMORIAM Gerhard Hochschild Professor of Mathematics, Emeritus UC Berkeley 1915 - 2010
- Ferrer Santos, Walter (2011). "Gerhard Hochschild (1915/2010) A Mathematician of the XXth Century". arXiv: .
- Ferrer Santos, Walter; Moskowitz, Martin, eds. (2011), "Gerhard Hochschild (1915-2010)" (PDF), Notices of the American Mathematical Society, 58 (8): 1078–1099, ISSN 0002-9920