JSTOR All-Stars: "Very Basic Lie Theory"

December 19, 2007

The JSTOR database is an archive of important scholarly journals, offering researchers high-resolution, scanned images of journal issues and pages. It now includes 37,094 articles from The American Mathematical Monthly, from 1894 to 2003. The 1983 article "Very Basic Lie Theory" by Roger Howe ranks as the ninth most frequently accessed Monthly article in the database.

"Very Basic Lie Theory"
Roger Howe
The American Mathematical Monthly, Vol. 90, No. 9 (November 1983), pp. 600-623

"Lie theory, the theory of Lie groups, Lie algebras and their applications, is a fundamental part of mathematics. Since World War II it has been the focus of a burgeoning research effort, and is now seen to touch a tremendous spectrum of mathematical areas, including classical, differential, and algebraic geometry, topology, ordinary and partial differential equations, complex analysis (one and several variables), group and ring theory, number theory, and physics, from classical to quantum and relativistic." This article presents an introduction to Lie theory at a level appropriate to advanced undergraduate instruction.

The top eight Monthly articles are:

  1. "College Admissions and the Stability of Marriage" by David Gale and Lloyd Shapley, Vol. 69, No. 1 (January, 1962), pp. 9-15.
  2. "Introduction to Fermat's Last Theorem" by David A. Cox, Vol. 101, No. 1 (January, 1994), pp. 3-14.
  3. "Period Three Implies Chaos" by Tien-Yien Li and James A Yorke, Vol. 82, No. 10 (December, 1975), pp. 985-992.
  4. "History of Mathematics Before the Seventeenth Century" by Raymond Clare Archibald, Vol. 56, No. 1 (January, 1949), pp. 7-34.
  5. "Galois Theory for Beginners" by John Stillwell, Vol. 101, No. 1 (January, 1994), pp. 22-27.
  6. "Can One Hear the Shape of a Drum?" by Mark Kac, Vol. 73, No. 4 (April 1966), pp. 1-23.
  7. "Mathematics and Sex" by John Ernest, Vol. 83, No. 8 (October 1966), pp. 595-614.
  8. "Hypatia and Her Mathematics" by Michael A.B. Deakin, Vol. 101, No. 3 (March 1994), pp. 234-243.

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