Wilhelm Killing
Wilhelm Karl Joseph Killing | |
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Born | 10 May 1847 |
Died | 11 February 1923 | (aged 75)
Citizenship | German |
Known for | Lie algebras, Lie groups, and non-Euclidean geometry |
Spouse | Anna Commer |
Awards | Lobachevsky Prize (1900) |
Scientific career | |
Fields | Mathematics |
Doctoral advisor | Karl Weierstrass Ernst Kummer |
Wilhelm Karl Joseph Killing (10 May 1847 – 11 February 1923) was a German mathematician who made important contributions to the theories of Lie algebras, Lie groups, and non-Euclidean geometry.
Life
Killing studied at the University of Münster and later wrote his dissertation under Karl Weierstrass and Ernst Kummer at Berlin in 1872. He taught in gymnasia (secondary schools) from 1868 to 1872. In 1875, he married Anna Commer, who was the daughter of a music lecturer. He became a professor at the seminary college Collegium Hosianum in Braunsberg (now Braniewo). He took holy orders in order to take his teaching position. He became rector of the college and chair of the town council. As a professor and administrator Killing was widely liked and respected. Finally, in 1892 he became a professor at the University of Münster.[1]
In 1886, Killing and his wife entered the
Work
In 1878 Killing wrote on
Killing invented Lie algebras independently of Sophus Lie around 1880. Killing's university library did not contain the Scandinavian journal in which Lie's article appeared. (Lie later was scornful of Killing, perhaps out of competitive spirit and claimed that all that was valid had already been proven by Lie and all that was invalid was added by Killing.) In fact Killing's work was less rigorous logically than Lie's, but Killing had much grander goals in terms of classification of groups, and made a number of unproven conjectures that turned out to be true. Because Killing's goals were so high, he was excessively modest about his own achievement.[citation needed]
From 1888 to 1890, Killing essentially classified the complex finite-dimensional
As A. J. Coleman says, "He exhibited the characteristic equation of the Weyl group when Weyl was 3 years old and listed the orders of the Coxeter transformation 19 years before Coxeter was born."[5]
Selected works
- Work on non-Euclidean geometry
- Killing, W. (1878) [1877]. "Ueber zwei Raumformen mit constanter positiver Krümmung". Journal für die reine und angewandte Mathematik. 86: 72–83.
- Killing, W. (1880) [1879]. "Die Rechnung in den Nicht-Euklidischen Raumformen". Journal für die reine und angewandte Mathematik. 89: 265–287.
- Killing, W. (1885) [1884]. "Die Mechanik in den Nicht-Euklidischen Raumformen". Journal für die reine und angewandte Mathematik. 98: 1–48.
- Killing, W. (1885). Die nicht-euklidischen Raumformen. Leipzig: Teubner.
- Killing, W. (1891). "Ueber die Clifford-Klein'schen Raumformen". Mathematische Annalen. 39 (2): 257–278. S2CID 119473479.
- Killing, W. (1892). "Ueber die Grundlagen der Geometrie". Journal für die reine und angewandte Mathematik. 109: 121–186.
- Killing, W. (1893). "Zur projectiven Geometrie". Mathematische Annalen. 43 (4): 569–590. S2CID 121748880.
- Killing, W. (1893). Einführung in die Grundlagen der Geometrie I. Paderborn: Schöningh.
- Killing, W. (1898) [1897]. Einführung in die Grundlagen der Geometrie II. Paderborn: Schöningh.
- Work on transformation groups
- Killing, W. (1888). "Die Zusammensetzung der stetigen endlichen Transformationsgruppen". Mathematische Annalen. 31 (2): 252–290. S2CID 120501356.
- Killing, W. (1889). "Die Zusammensetzung der stetigen endlichen Transformationsgruppen. Zweiter Theil". Mathematische Annalen. 33: 1–48. S2CID 124198118.
- Killing, W. (1889). "Die Zusammensetzung der stetigen endlichen Transformationsgruppen. Dritter Theil". Mathematische Annalen. 34: 57–122. S2CID 179177899.
- Killing, W. (1890). "Erweiterung des Begriffes der Invarianten von Transformationsgruppen". Mathematische Annalen. 35 (3): 423–432. S2CID 121050972.
- Killing, W. (1890). "Die Zusammensetzung der stetigen endlichen Transformationsgruppen. Vierter Theil". Mathematische Annalen. 36: 161–189. S2CID 179178061.
- Killing, W. (1890). "Bestimmung der grössten Untergruppen von endlichen Transformationsgruppen". Mathematische Annalen. 36 (2): 239–254. S2CID 121548146.
See also
- Killing equation
- Killing form
- Killing–Hopf theorem
- Killing horizon
- Killing spinor
- Killing tensor
- Killing vector field
- Levi decomposition
- G2 (mathematics)
- Root system
References
- ^ a b O'Conner, J. J.; Robertson, E. F. (February 2005). "Wilhelm Killing - Biography". MacTutor. Retrieved 2023-08-23.
- ISBN 0-387-98963-3.
- S2CID 124088818.
- ISBN 038794348X.)
{{cite book}}
: CS1 maint: location missing publisher (link - ^ Coleman, A. John, "The Greatest Mathematical Paper of All Time," The Mathematical Intelligencer, vol. 11, no. 3, pp. 29–38.
External links
- O'Connor, John J.; Robertson, Edmund F., "Wilhelm Killing", MacTutor History of Mathematics Archive, University of St Andrews
Media related to Wilhelm Killing (mathematician) at Wikimedia Commons