A. A. Albert Explained

A. A. Albert
Birth Name:	Abraham Adrian Albert
Birth Date:	9 November 1905
Birth Place:	Chicago, US
Death Place:	Chicago, US
Fields:	mathematics
Workplaces:	Columbia University University of Chicago
Alma Mater:	University of Chicago
Doctoral Advisor:	L. E. Dickson
Doctoral Students:	Richard Block Nathan Divinsky Murray Gerstenhaber Anatol Rapaport Richard D. Schafer Daniel Zelinsky
Known For:	Albert algebras
Awards:	Cole Prize (1939)

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.
.^[5]
A. A. Albert, Structure of algebras, 1939.^[6] Colloquium publications 24, American Mathematical Society, 2003, .
^[7]
- - ^[8]
with Rebeun Sandler: Book: Introduction to finite projective planes. 1968.

Articles in PNAS

The Norm Form of a Rational Division Algebra. Proc Natl Acad Sci U S A. 528485 . 16590045. 43. 1957. 506–9. 10.1073/pnas.43.6.506 . Albert. A. A.. 6. 1957PNAS...43..506A. free.
On Hermitian Operators over the Cayley Algebra. Proc Natl Acad Sci U S A. 528152 . 16589719. 41. 1955. 639–40. 10.1073/pnas.41.9.639 . Albert. A. A.. 9. 1955PNAS...41..639A. free.
A Note on the Exceptional Jordan Algebra. Proc Natl Acad Sci U S A. 1063206 . 15430315. 36. 1950. 372–4. 10.1073/pnas.36.7.372 . Albert. A. A.. 7. 1950PNAS...36..372A. free.
A Theory of Trace-Admissible Algebras. Proc Natl Acad Sci U S A. 1063026 . 16588897. 35. 1949. 317–22. 10.1073/pnas.35.6.317. Albert. A. A.. 6. 1949PNAS...35..317A. free.
The Minimum Rank of a Correlation Matrix. Proc Natl Acad Sci U S A. 1078686 . 16588638. 30. 1944. 144–6. 10.1073/pnas.30.6.144 . Albert. A. A.. 6. 1944PNAS...30..144A. free.
The Matrices of Factor Analysis. Proc Natl Acad Sci U S A. 1078675 . 16578117. 30. 1944. 90–5. 10.1073/pnas.30.4.90 . Albert. A. A.. 4. 1944PNAS...30...90A. free.
On the Structure of Pure Riemann Matrices with Non-commutative Multiplication Algebras. Proc Natl Acad Sci U S A. 526637 . 16587573. 16. 1930. 308–12. 10.1073/pnas.16.4.308. Albert. A. A.. 4. 1930PNAS...16..308A. free.
The Group of the Rank Equation of Any Normal Division Algebra. Proc Natl Acad Sci U S A. 1085796 . 16587420. 14. 1928. 906–7. 10.1073/pnas.14.12.906 . Albert. A. A.. 12. 1928PNAS...14..906A. free.
On the Nuclei of a Simple Jordan Algebra. Proc Natl Acad Sci U S A. 221198 . 16578544. 50. 1963. 446–7. 10.1073/pnas.50.3.446 . Albert. A. A.. 3. 1963PNAS...50..446A. free.
A Property of Special Jordan Algebras. Proc Natl Acad Sci U S A. 534263 . 16589918. 42. 1956. 624–5. 10.1073/pnas.42.9.624 . Albert. A. A.. 9. 1956PNAS...42..624A. free.
On Involutorial Algebras. Proc Natl Acad Sci U S A. 528119 . 16589700. 41. 1955. 480–2. 10.1073/pnas.41.7.480 . Albert. A. A.. 7. 1955PNAS...41..480A. free.
Involutorial Simple Algebras and Real Riemann Matrices. Proc Natl Acad Sci U S A. 1076512 . 16587930. 20. 1934. 676–81. 10.1073/pnas.20.12.676 . Albert. A. A.. 12. 1934PNAS...20..676A. free.
Normal Division Algebras of 2^2m. Proc Natl Acad Sci U S A. 1076070 . 16587641. 17. 1931. 389–92. 10.1073/pnas.17.6.389 . Albert. A. A.. 6. free.
On Direct Products, Cyclic Division Algebras, and Pure Riemann Matrices. Proc Natl Acad Sci U S A. 526638 . 16587574. 16. 1930. 313–5. 10.1073/pnas.16.4.313. Albert. A. A.. 4. 1930PNAS...16..313A. free.
The Rank Function of Any Simple Algebra. Proc Natl Acad Sci U S A. 522469 . 16587486. 15. 1929. 372–6. 10.1073/pnas.15.4.372 . Albert. A. A.. 4. 1929PNAS...15..372A. free.
Normal Division Algebras Satisfying Mild Assumptions. Proc Natl Acad Sci U S A. 1085795 . 16587419. 14. 1928. 904–6. 10.1073/pnas.14.12.904 . Albert. A. A.. 12. 1928PNAS...14..904A. free.

External links

- - 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
Guide to the Abraham Adrian Albert Papers 1921-2004 from the University of Chicago Special Collections Research Center

Notes and References

Web site: Jewish Mathematicians.
http://www.jinfo.org/Cole_Mathematics.html Jewish recipients of the Frank Nelson Cole Prizes in algebra and number theory (43% of recipients)
Web site: Abraham Adrian Albert: 1905–1972. Kaplansky. Irving. Irving Kaplansky. Celebratio Mathematica. Mathematical Sciences Publishers. 2023-11-04.
Web site: Book of Members, 1780-2010: Chapter A. American Academy of Arts and Sciences. 6 April 2011. https://web.archive.org/web/20110510021801/http://www.amacad.org/publications/BookofMembers/ChapterA.pdf. 10 May 2011 . live.
Brinkmann, H. W.. Review: Modern Higher Algebra by A. Adrian Albert. Bull. Amer. Math. Soc.. 1938. 44. 7. 471–473. 10.1090/s0002-9904-1938-06758-4. free.
Baer, Reinhold. Reinhold Baer. Review: A. Adrian Albert, Structure of Algebras. Bull. Amer. Math. Soc.. 1940. 46. 7. 587–591. 10.1090/s0002-9904-1940-07233-7. free.
1941. Review of Introduction to algebraic theories by A. Adrian Albert. The Mathematical Gazette. 25. 265. 184. 10.2307/3607394. 3607394. 4088670 .
Mattuck, Arthur. Review: Fundamental concepts of higher algebra by A. Adrian Albert. Bull. Amer. Math. Soc.. 1957. 63. 5. 323–325. 10.1090/s0002-9904-1957-10130-x. free.