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

- Journal title : Journal for History of Mathematics
- Volume 29, Issue 3, 2016, pp.157-172
- Publisher : The Korean Society for History of Mathematics
- DOI : 10.14477/jhm.2016.29.3.157

Title & Authors

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

Kim, Young Wook; Lee, Jin Ho;

Kim, Young Wook; Lee, Jin Ho;

Abstract

Sophus Lie`s research is regarded as one of the most important mathematical advancements in the 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

Sophus Lie;Felix C. Klein;line geometry;line complex;transformation group;infinitesimal transformation group;differential equation;

Language

Korean

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