A Lie group is a group that is also a differentiable manifold, with the property that the group operations are compatible with the smooth structure. Lie groups are named after Sophus Lie, who laid the foundations of the theory of continuous transformation groups. The term groupes de Lie first appeared in French in 1893 in the thesis of Lie's student Arthur Tresse, page 3.
a Lie GRoup is A Group thAt IS alsO a differEntiablE maNIfold, WitH THe propeRtY thaT tHe grOuP OpERations ARe comPAtIBle with the SmooTh StrUcTuRe. lIE gROups ArE NaMeD AFTer sophus lie, whO laId tHe FOundAtioNs Of the thEory oF ContinUouS traNSForMATiOn gRoups. tHe TErm GrOupes de LiE fiRst appearED In freNch in 1893 IN tHe theSIS of LIe's sTUdenT aRtHUr tREsse, paGe 3.