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Gerhard Hochschild

November 10, 2023

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
BornApril 29, 1915
Berlin, Germany
DiedJuly 8, 2010 (age 95)
El Cerrito, California
CitizenshipGerman
American
OccupationMathematician
SpouseRuth Heinsheimer
Children2
Parent(s)Lilli and Heinrich Hochschild

Early life edit

On April 29, 1915, Hochschild was born to a middle-class Jewish family in Berlin, Germany,[1][2] the son of Lilli and Heinrich Hochschild.[3] Hochschild had an older brother.[1] His father was a patent attorney who had an engineering degree. After the rise of the National Socialist German Workers' Party in 1933, his father sent him to South Africa where he was able to enroll in school with funding from the Hochschild Family Foundation established by Berthold Hochschild, a cousin of his grandfather.[4]

Education edit

In 1936, Hochschild earned a BS degree in mathematics from University of Cape Town in Union of South Africa.[1] In 1937, Hochschild earned a MS degree in mathematics from University of Cape Town.[1] In 1941, Hochschild earned his PhD in mathematics from Princeton University.[1] Hochschild completed his thesis in 1941 at Princeton University with Claude Chevalley on Semisimple Algebras and Generalized Derivations.

Career edit

In 1956–7 Hochschild was at the Institute for Advanced Study. Hochschild was a professor at University of Illinois at Urbana-Champaign. In the late 1950s Hochschild was a professor at 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.[5]

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

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

In 1982, Hochschild retired but continued teaching part-time until 1985.[1]

Personal life edit

In July 1950, Hochschild married Ruth Heinsheimer.[6] Ruth was born in Germany and fled with her mother in 1939; the couple met at the University of Illinois where she was earning her M.S. in mathematics and Gerhard was working as an assistant professor.[7] Hochschild's children are Ann Hochschild (b. 1955) and Peter Hochschild (b. 1957).[1][8]

On July 8, 2010, Hochschild died at his home. Hochschild was 95.[1]

See also edit

Publications edit

  • Hochschild, G. (1945), "On the cohomology groups of an associative algebra", Annals of Mathematics, Second Series, 46 (1): 58–67, doi:10.2307/1969145, ISSN 0003-486X, JSTOR 1969145, MR 0011076
  • Hochschild, G.; Nakayama, Tadasi (1952), "Cohomology in class field theory", Annals of Mathematics, Second Series, 55 (2): 348–366, doi:10.2307/1969783, 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, vol. 75, Berlin, New York: Springer-Verlag, ISBN 978-0-387-90541-9, MR 0620024
  • Hochschild, Gerhard Paul (1983), Perspectives of elementary mathematics, Berlin, New York: Springer-Verlag, ISBN 978-0-387-90848-9, MR 0710303

References edit

  1. ^ a b c d e f g h "IN MEMORIAM Gerhard Hochschild". universityofcalifornia.edu. Retrieved December 22, 2018.
  2. ^ Moscowitz, p. 1081
  3. ^ Moscowitz, p. 1082
  4. ^ Moscowitz, p. 1082
  5. ^ Porter, Tim (April 8, 2014), "Hochschild-Kostant-Rosenberg theorem", nLab.
  6. ^ Moscowitz, p. 1087
  7. ^ Moscowitz, p. 1087
  8. ^ Moscowitz, p. 1087
  • Moore, Calvin C.; Ribet, Kenneth A.; Wolf, Joseph A. (2011), , archived from the original on 2011-09-15
  • Ferrer Santos, Walter (2011). "Gerhard Hochschild (1915/2010) A Mathematician of the XXth Century". arXiv:1104.0335 [math.HO].
  • Moskowitz, Martin; Ferrer Santos, Walter, eds. (2011), "Gerhard Hochschild (1915-2010)" (PDF), Notices of the American Mathematical Society, 58 (8): 1078–1099, ISSN 0002-9920

External links edit

 
Wikiquote has quotations related to Gerhard Hochschild.
 
Scholia has a profile for Gerhard Hochschild (Q371662).

November 10, 2023
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This article includes a list of general references but it lacks sufficient corresponding inline citations Please help to improve this article by introducing more precise citations February 2013 Learn how and when to remove this template message 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 HochschildGerhard HochschildBornApril 29 1915Berlin GermanyDiedJuly 8 2010 age 95 El Cerrito CaliforniaCitizenshipGerman AmericanOccupationMathematicianSpouseRuth HeinsheimerChildren2Parent s Lilli and Heinrich Hochschild Contents 1 Early life 2 Education 3 Career 4 Personal life 5 See also 6 Publications 7 References 8 External linksEarly life editOn April 29 1915 Hochschild was born to a middle class Jewish family in Berlin Germany 1 2 the son of Lilli and Heinrich Hochschild 3 Hochschild had an older brother 1 His father was a patent attorney who had an engineering degree After the rise of the National Socialist German Workers Party in 1933 his father sent him to South Africa where he was able to enroll in school with funding from the Hochschild Family Foundation established by Berthold Hochschild a cousin of his grandfather 4 Education editIn 1936 Hochschild earned a BS degree in mathematics from University of Cape Town in Union of South Africa 1 In 1937 Hochschild earned a MS degree in mathematics from University of Cape Town 1 In 1941 Hochschild earned his PhD in mathematics from Princeton University 1 Hochschild completed his thesis in 1941 at Princeton University with Claude Chevalley on Semisimple Algebras and Generalized Derivations Career editIn 1956 7 Hochschild was at the Institute for Advanced Study Hochschild was a professor at University of Illinois at Urbana Champaign In the late 1950s Hochschild was a professor at University of California Berkeley Hochschild 1945 introduced Hochschild cohomology a cohomology theory for algebras which classifies deformations of algebras Hochschild amp 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 5 Among his students were Andrzej Bialynicki Birula and James Ax In 1955 Hochschild was a Guggenheim Fellow In 1979 Hochschild was elected to the National Academy of Sciences and in 1980 he was awarded the Leroy P Steele Prize of the AMS In 1982 Hochschild retired but continued teaching part time until 1985 1 Personal life editIn July 1950 Hochschild married Ruth Heinsheimer 6 Ruth was born in Germany and fled with her mother in 1939 the couple met at the University of Illinois where she was earning her M S in mathematics and Gerhard was working as an assistant professor 7 Hochschild s children are Ann Hochschild b 1955 and Peter Hochschild b 1957 1 8 On July 8 2010 Hochschild died at his home Hochschild was 95 1 See also editHochschild Mostow groupPublications editHochschild G 1945 On the cohomology groups of an associative algebra Annals of Mathematics Second Series 46 1 58 67 doi 10 2307 1969145 ISSN 0003 486X JSTOR 1969145 MR 0011076 Hochschild G Nakayama Tadasi 1952 Cohomology in class field theory Annals of Mathematics Second Series 55 2 348 366 doi 10 2307 1969783 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 vol 75 Berlin New York Springer Verlag ISBN 978 0 387 90541 9 MR 0620024 Hochschild Gerhard Paul 1983 Perspectives of elementary mathematics Berlin New York Springer Verlag ISBN 978 0 387 90848 9 MR 0710303References edit a b c d e f g h IN MEMORIAM Gerhard Hochschild universityofcalifornia edu Retrieved December 22 2018 Moscowitz p 1081 Moscowitz p 1082 Moscowitz p 1082 Porter Tim April 8 2014 Hochschild Kostant Rosenberg theorem nLab Moscowitz p 1087 Moscowitz p 1087 Moscowitz p 1087 Moore Calvin C Ribet Kenneth A Wolf Joseph A 2011 IN MEMORIAM Gerhard Hochschild Professor of Mathematics Emeritus UC Berkeley 1915 2010 archived from the original on 2011 09 15 Ferrer Santos Walter 2011 Gerhard Hochschild 1915 2010 A Mathematician of the XXth Century arXiv 1104 0335 math HO Moskowitz Martin Ferrer Santos Walter eds 2011 Gerhard Hochschild 1915 2010 PDF Notices of the American Mathematical Society 58 8 1078 1099 ISSN 0002 9920External links edit nbsp Wikiquote has quotations related to Gerhard Hochschild nbsp Scholia has a profile for Gerhard Hochschild Q371662 Gerhard Hochschild at the Mathematics Genealogy Project Pictures of Gerhard Hochschild from Oberwolfach Finding Aid to the Gerhard P Hochschild papers 1941 2004 The Bancroft Library Hochschild Family Foundation at foundation center org Retrieved from https en wikipedia org w index php title Gerhard Hochschild amp oldid 1171018135, wikipedia, wiki, book, books, library,

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