Abraham Adrian Albert

Abraham Adrian Albert (November 9, 1905 – June 6, 1972) was an American mathematician.^[1] In 1939, he received the American Mathematical Society's Cole Prize in Algebra for his work on Riemann matrices.^[2] He is best known for his work on the Albert–Brauer–Hasse–Noether theorem on finite-dimensional division algebras over number fields and as the developer of Albert algebras, which are also known as exceptional Jordan algebras.

Professional overview

A second generation American, he was born in Guatemala City and most associated with that city. He received his Bachelor of Science in 1926, Masters in 1927, and PhD in 1928, at the age of 22. All degrees were obtained from the University of Chicago. He married around the same time as his graduation. He spent his postdoctoral year at Princeton University and then from 1929 to 1931 he was an instructor at Columbia University. During this period he worked on Abelian varieties and their endomorphism algebras. He returned to Princeton for the opening year of the Institute for Advanced Study in 1933-34 and spent another year in Princeton in 1961-62 as the first Director of the Communications Research Division of IDA (the Institute for Defense Analyses).

From 1931 to 1972, he served on the mathematics faculty at the University of Chicago, where he became chair of the Mathematics Department in 1958 and Dean of the Physical Sciences Division in 1961.

As a research mathematician, he is primarily known for his work as one of the principal developers of the theory of linear associative algebras and as a pioneer in the development of linear non-associative algebras, although all of this grew out of his work on endomorphism algebras of Abelian varieties.

As an applied mathematician, he also did work for the military during World War II and thereafter. One of his most notable achievements was his groundbreaking work on cryptography. He prepared a manuscript, "Some Mathematical Aspects of Cryptography," for his invited address at a meeting of the American Mathematical Society in November 1941. The theory that developed from this work can be seen in digital communications technologies.

After WWII, he became a forceful advocate favoring government support for research in mathematics on a par with other physical sciences. He served on policy-making bodies at the Office of Naval Research, the United States National Research Council, and the National Science Foundation that funneled research grants into mathematics, giving many young mathematicians career opportunities previously unavailable. Due to his success in helping to give mathematical research a sound financial footing, he earned a reputation as a "statesman for mathematics." Albert was elected a Fellow of the American Academy of Arts and Sciences in 1968.^[3]

Publications

Books

• A. A. Albert, Algebras and their radicals, and division algebras, 1928.
• A. A. Albert, Modern higher algebra, 1937.^[4]
• A. A. Albert, Structure of algebras, 1939.^[5] Colloquium publications 24, American Mathematical Society, 2003, ISBN 0-8218-1024-3.
• Introduction to algebraic theories. 1941. 
• College algebra. 1946. 
• Solid analytic geometry. 1949. 
• Fundamental concepts of higher algebra. 1956. ^[6]
• with Rebeun Sandler: Introduction to finite projective plans. 1968. 
• Albert, A. Adrian (1993), Block, Richard E.; Jacobson, Nathan; Osborn, J. Marshall; Saltman, David J.; Zelinsky, Daniel, eds., Collected mathematical papers. Part 1. Associative algebras and Riemann matrices., Providence, R.I.: American Mathematical Society, ISBN 978-0-8218-0005-8, MR 1213451 
• Albert, A. Adrian (1993), Block, Richard E.; Jacobson, Nathan; Osborn, J. Marshall; Saltman, David J.; Zelinsky, Daniel, eds., Collected mathematical papers. Part 2. Nonassociative algebras and miscellany, Providence, R.I.: American Mathematical Society, ISBN 978-0-8218-0007-2, MR 1213452 

Articles in PNAS

• "The Norm Form of a Rational Division Algebra". Proc Natl Acad Sci U S A. PMC 528485.  1957 June 15; 43(6): 506–509.
• "On Hermitian Operators over the Cayley Algebra". Proc Natl Acad Sci U S A. PMC 528152.  1955 September 15; 41(9): 639–640.
• "A Note on the Exceptional Jordan Algebra". Proc Natl Acad Sci U S A. PMC 1063206.  1950 July; 36(7): 372–374.
• "A Theory of Trace-Admissible Algebras". Proc Natl Acad Sci U S A. PMC 1063026.  1949 June; 35(6): 317–322.
• "The Minimum Rank of a Correlation Matrix". Proc Natl Acad Sci U S A. PMC 1078686.  1944 June 15; 30(6): 144–146.
• "The Matrices of Factor Analysis". Proc Natl Acad Sci U S A. PMC 1078675.  1944 April 15; 30(4): 90–95.
• "On the Structure of Pure Riemann Matrices with Non-commutative Multiplication Algebras". Proc Natl Acad Sci U S A. PMC 526637.  1930 April 15; 16(4): 308–312.
• "The Group of the Rank Equation of Any Normal Division Algebra". Proc Natl Acad Sci U S A. PMC 1085796.  1928 December; 14(12): 906–907.
• "On the Nuclei of a Simple Jordan Algebra". Proc Natl Acad Sci U S A. PMC 221198.  1963 September; 50(3): 446–447.
• "A Property of Special Jordan Algebras". Proc Natl Acad Sci U S A. PMC 534263.  1956 September; 42(9): 624–625.
• "On Involutorial Algebras". Proc Natl Acad Sci U S A. PMC 528119.  1955 July 15; 41(7): 480–482.
• "Involutorial Simple Algebras and Real Riemann Matrices". Proc Natl Acad Sci U S A. PMC 1076512.  1934 December; 20(12): 676–681.
• "Normal Division Algebras of 2^2m ". Proc Natl Acad Sci U S A. PMC 1076070.  1931 June; 17(6): 389–392.
• "On Direct Products, Cyclic Division Algebras, and Pure Riemann Matrices". Proc Natl Acad Sci U S A. PMC 526638.  1930 April 15; 16(4): 313–315.
• "The Rank Function of Any Simple Algebra". Proc Natl Acad Sci U S A. PMC 522469.  1929 April 15; 15(4): 372–376.
• "Normal Division Algebras Satisfying Mild Assumptions". Proc Natl Acad Sci U S A. PMC 1085795.  1928 December; 14(12): 904–906.

References

Further reading

• Nancy E. Albert, A³ and His Algebra: How a Boy from Chicago's West Side Became a Force in American Mathematics, iUniverse, Lincoln, NE, 2005. ISBN 978-0-595-32817-8.

External links

• Abraham Adrian Albert at the Mathematics Genealogy Project
• O'Connor, John J.; Robertson, Edmund F., "Abraham Adrian Albert", MacTutor History of Mathematics archive, University of St Andrews .
• Abraham Adrian Albert 1905–1972, A Biographical Memoir by Irving Kaplansky
• National Academy of Sciences Biographical Memoir
• search on author Abraham Adrian Albert from Google Scholar