Sophus Lie, the mathematician

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[4] Bourbaki, N., tlements de mathematiques. FaccXXXVII. Groupes etAlgebres de Lie (Ch. II-III). Hermann, Paris, 1972.[5] Cartan, ., Les systemes de Pfaff a cinq variables et les 6quations auxderives partielles du second ordre. Ann. Ec. Norrnale 27 (1910), 109192.[6] Cartan, E., Sur l'equivalence absolue de certains systbmes d'6quationsdifferentiels et sur certaines families de courbes. Bull. Soc. Math. France42 (1914), 12-48.[7] Cartan, E., Sur l'int6gration de certains systemes ind6terminesd'6quations diffrentielles. J. Reine Angew. Math. 145 (1915), 86-91.[8] Cartan, E., A Centenary: Sophus Lie. In "Great Currents of MathematicalThought" F. Le Lionnais (Ed). Dover, New York, 1971, 262-267.11[9] Cartan, E., Oevres Completes, Gauthier-Villars, Paris 1952.[10] Cecil, T. E., Lie Sphere Geometry. Springer-Verlag, New York, 1992.[11] Darboux, G., Theorie G6nerale des Surfaces, Vol. I-IV. Gauthier Villars,Paris 1887-1896.II[12] Engel, F., Sophus Lie (obituary). Jber. Deutsch. Math.-Verein 8 (1900),30-46.[13] Gonzalez-Lopez, A., Karmran, N., and Olver, P. J., Lie algebras of vector.fields in the plane. Proc. London Math. Soc. (to appear).[14] Hawkins, T., Line geometry, differential equations, and the birth of Lie'stheory of groups. In "The History of Modern Mathematics" D. E. Roweand J. McCleary, eds. Academic Press, New York, 1989.[15] Helgason, S., Differential operators on homogeneous spaces. Acta Math.102 (1959), 239-299.[16] Helgason, S., Invariant differential equations on homogeneous manifolds.Bull. Amer. Math. Soc. 83 (1977), 751-774.[17] Hilbert, D., Ujber d Begriff der Klasse von Differentialgleichungen.AMath. Ann. 73 (1912), 95-108.[18] Klein, F., Vorlesungen iiber Hdhere Geometrie, Springer, Berlin 1926.[19] Klein, F., Gesammelte Mathematische Abhandlungen, Vol. I-III, Berlin1921-1923.Zoc
[201 Lie, S., Zur Theorie des Integrabilitetsfaktors, Christiania Forh. 1874,242-254; reprint in [22], Vol. III, no. XIII, pp. 176-187.[211 Lie, S., Verallgemeinerung und neue Verwertung der Jacobischen Multiplikatortheorie,Christiania Forh. 1874, 254-274.[22] Lie, S., Gesammelte Abhandlungen, 7 Vols. Teubner, Leipzig, 1922-1960.[23] Lie, S., and Engel, F., Theorie de Transformationsgruppen, 3 vols, Teubner,Leipzig 1888-1893.[24] Mostow, G. D., Continuous groups, Encyclopaedia Britannica, 1967.[25] Olver, P., Applications of Lie Groups to Differential Equations. SpringerVerlag, New York 1986.[26] Pommaret, J. F., Differential Galois Theory, Gordon and Breach, NewYork, 1983.21
Page 1 and 2: Courtesy of Scandinavian University
Page 3 and 4: P = P12P34+ P13P42 + P14P23 = 0 T
Page 5 and 6: Note that points are included (A =
Page 7 and 8: this meant that the asymptotic curv
Page 9 and 10: (F,g) = 0which enters in Jacobi's w
Page 11 and 12: where (u) = (l, .. ., Ur) depends a
Page 13 and 14: happiest of his life. Lie decided t
Page 15 and 16: when rigorization of differential g
Page 17: and analysed it is hard to do so in

Sophus Lie, the mathematician

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