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;

Abstract
Sophus Lie`s research is regarded as one of the most important mathematical advancements in the $\small{19^{th}}$ 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
Sophus Lie;Felix C. Klein;line geometry;line complex;transformation group;infinitesimal transformation group;differential equation;
Language
Korean
Cited by
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