American mathematician (1905–1972)
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 first generation
American , he was born in
Chicago 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 the
Institute for Defense Analyses (IDA). He later served on the Board of Trustees of IDA 1969-1972.
[3]
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 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.
[4]
Publications
Books
A. A. Albert, Algebras and their radicals, and division algebras , 1928.
Albert, A. Adrian (2015) [1938],
Modern higher algebra ,
Cambridge University Press ,
ISBN
978-1-107-54462-8 .
[5]
A. A. Albert, Structure of algebras , 1939.
[6] Colloquium publications 24 ,
American Mathematical Society , 2003,
ISBN
0-8218-1024-3 .
Introduction to algebraic theories , 1941
[7]
College algebra , 1946
Solid analytic geometry , 1949
Fundamental concepts of higher algebra , 1956
[8]
with Rebeun Sandler: Introduction to finite projective planes . 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
Albert, A. A. (1957).
"The Norm Form of a Rational Division Algebra" . Proc Natl Acad Sci U S A . 43 (6): 506–9.
Bibcode :
1957PNAS...43..506A .
doi :
10.1073/pnas.43.6.506 .
PMC
528485 .
PMID
16590045 .
Albert, A. A. (1955).
"On Hermitian Operators over the Cayley Algebra" . Proc Natl Acad Sci U S A . 41 (9): 639–40.
Bibcode :
1955PNAS...41..639A .
doi :
10.1073/pnas.41.9.639 .
PMC
528152 .
PMID
16589719 .
Albert, A. A. (1950).
"A Note on the Exceptional Jordan Algebra" . Proc Natl Acad Sci U S A . 36 (7): 372–4.
Bibcode :
1950PNAS...36..372A .
doi :
10.1073/pnas.36.7.372 .
PMC
1063206 .
PMID
15430315 .
Albert, A. A. (1949).
"A Theory of Trace-Admissible Algebras" . Proc Natl Acad Sci U S A . 35 (6): 317–22.
Bibcode :
1949PNAS...35..317A .
doi :
10.1073/pnas.35.6.317 .
PMC
1063026 .
PMID
16588897 .
Albert, A. A. (1944).
"The Minimum Rank of a Correlation Matrix" . Proc Natl Acad Sci U S A . 30 (6): 144–6.
Bibcode :
1944PNAS...30..144A .
doi :
10.1073/pnas.30.6.144 .
PMC
1078686 .
PMID
16588638 .
Albert, A. A. (1944).
"The Matrices of Factor Analysis" . Proc Natl Acad Sci U S A . 30 (4): 90–5.
Bibcode :
1944PNAS...30...90A .
doi :
10.1073/pnas.30.4.90 .
PMC
1078675 .
PMID
16578117 .
Albert, A. A. (1930).
"On the Structure of Pure Riemann Matrices with Non-commutative Multiplication Algebras" . Proc Natl Acad Sci U S A . 16 (4): 308–12.
Bibcode :
1930PNAS...16..308A .
doi :
10.1073/pnas.16.4.308 .
PMC
526637 .
PMID
16587573 .
Albert, A. A. (1928).
"The Group of the Rank Equation of Any Normal Division Algebra" . Proc Natl Acad Sci U S A . 14 (12): 906–7.
Bibcode :
1928PNAS...14..906A .
doi :
10.1073/pnas.14.12.906 .
PMC
1085796 .
PMID
16587420 .
Albert, A. A. (1963).
"On the Nuclei of a Simple Jordan Algebra" . Proc Natl Acad Sci U S A . 50 (3): 446–7.
Bibcode :
1963PNAS...50..446A .
doi :
10.1073/pnas.50.3.446 .
PMC
221198 .
PMID
16578544 .
Albert, A. A. (1956).
"A Property of Special Jordan Algebras" . Proc Natl Acad Sci U S A . 42 (9): 624–5.
Bibcode :
1956PNAS...42..624A .
doi :
10.1073/pnas.42.9.624 .
PMC
534263 .
PMID
16589918 .
Albert, A. A. (1955).
"On Involutorial Algebras" . Proc Natl Acad Sci U S A . 41 (7): 480–2.
Bibcode :
1955PNAS...41..480A .
doi :
10.1073/pnas.41.7.480 .
PMC
528119 .
PMID
16589700 .
Albert, A. A. (1934).
"Involutorial Simple Algebras and Real Riemann Matrices" . Proc Natl Acad Sci U S A . 20 (12): 676–81.
Bibcode :
1934PNAS...20..676A .
doi :
10.1073/pnas.20.12.676 .
PMC
1076512 .
PMID
16587930 .
Albert, A. A. (1931).
"Normal Division Algebras of 22m " . Proc Natl Acad Sci U S A . 17 (6): 389–92.
doi :
10.1073/pnas.17.6.389 .
PMC
1076070 .
PMID
16587641 .
Albert, A. A. (1930).
"On Direct Products, Cyclic Division Algebras, and Pure Riemann Matrices" . Proc Natl Acad Sci U S A . 16 (4): 313–5.
Bibcode :
1930PNAS...16..313A .
doi :
10.1073/pnas.16.4.313 .
PMC
526638 .
PMID
16587574 .
Albert, A. A. (1929).
"The Rank Function of Any Simple Algebra" . Proc Natl Acad Sci U S A . 15 (4): 372–6.
Bibcode :
1929PNAS...15..372A .
doi :
10.1073/pnas.15.4.372 .
PMC
522469 .
PMID
16587486 .
Albert, A. A. (1928).
"Normal Division Algebras Satisfying Mild Assumptions" . Proc Natl Acad Sci U S A . 14 (12): 904–6.
Bibcode :
1928PNAS...14..904A .
doi :
10.1073/pnas.14.12.904 .
PMC
1085795 .
PMID
16587419 .
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
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