Journal for History of Mathematics (한국수학사학회지)

The Korean Society for History of Mathematics (한국수학사학회)
권호 표지
DOI QR코드

DOI QR Code

Development of Geometry in the 19th century and Birth of Lie's theory of Groups

19세기 기하학의 발달과 리군론의 시작

  • Received : 2016.06.16
  • Accepted : 2016.06.29
  • Published : 2016.06.30
Download PDF
⟨ Previous Next ⟩

Abstract

Sophus Lie's research is regarded as one of the most important mathematical advancements in the $19^{th}$ century. His pioneering research in the field of differential equations resulted in an invaluable consolidation of calculus and group theory. Lie's group theory has been investigated and constantly modified by various mathematicians which resulted in a beautifully abstract yet concrete theory. However Lie's early intentions and ideas are lost in the mists of modern transfiguration. In this paper we explore Lie's early academic years and his object of studies which clarify the ground breaking ideas behind his theory.

Keywords

References

  1. BRYANT, R., An introduction to Lie groups and symplectic geometry, Park City, 24 June-20 July 1991.
  2. BRYANT, R., Griffiths, P., Grossman, D., Exterior Differential Systems and Euler-Lagrange Partial Differential Equations, U. of Chicago Press, 2003.
  3. COHEN, A., An introduction to the Lie theory of one-parameter groups, G. E. Stechert Co., 1911.
  4. COOLIDGE, J., A history of geometrical methods, Oxford U. P., 1940.
  5. DOLGACHEV, I. V., Classical algebraic geometry: a modern view, Cambridge U. P., 2012.
  6. GRAY, J. J., Linear differential equations and group theory from Riemann to Poincare, Birkhauser, 2000.
  7. HARTSHORNE, R., Teaching Geometry According to Euclid, Notices of the AMS 47 (4) (2000), 460-465.
  8. HAWKINS, T., Emergence of the theory of Lie groups, Springer, 2000.
  9. HAWKINS, T., Line Geometry, Differential Equations, and the Birth of Lie's Theory of Groups, in ROWE, D. E. and MCCLEARY, J. (Eds.), The history of Modern Mathematics, Vol. I: Ideas and Their Reception, Academic Press, 1989.
  10. HERMANN, R., Sophus Lie's 1880 transformation group paper, Math Sci Press, 1975.
  11. KLEIN F., Development of mathematics in the 19th century. 한경혜 역, 19세기 수학의 발전에 대한 강의, 나남, 2012.
  12. ROWE D. E., The early Geometrical Works of Sophus Lie and Felix Klein, in ROWE D. E. and MCCLEARY, J. (Eds.), The history of Modern Mathematics, Vol. I: Ideas and Their Reception, Academic Press, 1989.
  13. SEMPLE J. G., KNEEBONE, G. T., Algebraic Projective Geometry, Oxford U. P., 1952.
  14. Wikipedia, 영문판 위키피디아, https://en.wikipedia.org/wiki/Sophus_Lie, (30 May, 2016).