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Gerhard Hochschild

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Name
  
Gerhard Hochschild


Role
  
Mathematician

Gerhard Hochschild httpsmathberkeleyedusitesdefaultfilesimag

Died
  
July 8, 2010, El Cerrito, California, United States

Education
  
Princeton University (1938–1941)

Books
  
Introduction to Affine Algebraic Groups

Awards
  
Guggenheim Fellowship for Natural Sciences, US & Canada

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.

Gerhard Hochschild Gerhard Hochschild Wikipedia

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.

Gerhard Hochschild httpsuploadwikimediaorgwikipediacommonsthu

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.

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.

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 

    • References

    Gerhard Hochschild Wikipedia
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