19세기 기하학의 발달과 리군론의 시작

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김영욱;이진호
Kim, Young Wook;Lee, Jin Ho

  • 투고 : 2016.06.16
  • 심사 : 2016.06.29
  • 발행 : 2016.06.30

초록

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.

키워드

소푸스 리;페릭스 클라인;선기하학;선복합체;변환군;미소변환군;미분방정식

참고문헌

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  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.
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  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).

과제정보

연구 과제번호 : BK21플러스

연구 과제 주관 기관 : 고려대학교