Abraham Adrian Albert

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Abraham Adrian Albert (born November 9, 1905 in Chicago ; † June 6, 1972 ibid) was an American mathematician who studied algebra.

life and work

Albert's parents immigrated to the USA, his father from England, his mother from Russia. He studied at the University of Chicago , where he received his bachelor's degree in 1926 and his master's degree in 1927, where he received his doctorate from Leonard Dickson in 1928 ( Algebras and their Radicals and Division Algebras ). After completing his doctorate, he spent a year as a fellow of the National Research Council at Princeton University with Solomon Lefschetz and was an instructor at Columbia University from 1929 to 1931 . From 1931 he was at the University of Chicago until his retirement (1931 assistant professor, 1937 associate professor, 1941 professor), where he was dean of the mathematics faculty from 1958 to 1962 and dean of the physical sciences division from 1961 to 1971.

Albert worked on Riemann matrices (at the suggestion of Lefschetz) and linear associative algebras and non-associative algebras (from 1942). He first dealt with the Jordan algebras introduced by Pascual Jordan in studies of quantum mechanics in 1934 in On certain algebras of quantum mechanics . An exceptional Jordan algebra is named after him. Already in his dissertation he dealt with the classification of divisional algebras, which was started by Joseph Wedderburn . Here, however, he had competition in Germany from Helmut Hasse , Emmy Noether and Richard Brauer , who got ahead of him with the sentence by Brauer-Hasse-Noether.

During the Second World War he worked as an applied mathematician for the US government at Northwestern University and also in cryptography . After the war, he held numerous positions as a government advisor and was particularly responsible for the extensive award of government grants and contracts for mathematical research. From 1958 to 1961 he was chairman of the mathematics department of the National Research Council.

In 1939 he received the Cole Prize of the American Mathematical Society (AMS) for his work on Riemann matrices in the Annals of Mathematics 1934/35. In 1943 he was accepted into the National Academy of Sciences , in 1952 in the Brazilian and in 1963 in the Argentine Academy of Sciences and in 1968 in the American Academy of Arts and Sciences . 1956/56 he was President of the American Mathematical Society. In 1950 he gave a plenary lecture at the International Congress of Mathematicians in Cambridge (Massachusetts) (Power-Associative Algebras).

Anatol Rapoport is one of his doctoral students .

He had been married since 1927 and had three children.

Works (selection)

  • Modern higher algebra. 1937
  • Structure of Algebras. 1939, AMS, 2003
  • Collected Mathematical Papers. 2 volumes, AMS 1993

literature

  • Nancy E. Albert: and His Algebra: How a Boy from Chicago's West Side Became a Force in American Mathematics. New York, 2005.
  • Nathan Jacobson , Obituary in Bulletin of the AMS, Vol. 80, 1974, p. 1075
  • D. Zelinsky: Albert. American Mathematical Monthly, Vol. 80, 1973, p. 661
  • Irving Kaplansky : AAAlbert. In: A century of mathematics in America. Vol. 1, AMS, 1988, (in AMS History of Mathematics, Vol. 1, online here )
  • Karen Parshall : AAAlbert , in the Supplementary Volumes of the Dictionary of Scientific Biography , 1990

Remarks

  1. According to Bernhard Riemann, they characterize the lattices that can occur as period lattices of Riemann surfaces , but not completely. The complete characterization is the so-called Schottky problem.

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