Matches in DBpedia 2016-04 for { <http://dbpedia.org/resource/Wilhelm_Killing> ?p ?o }
- Wilhelm_Killing abstract "Wilhelm Karl Joseph Killing (May 10, 1847– February 11, 1923) was a German mathematician who made important contributions to the theories of Lie algebras, Lie groups, and non-Euclidean geometry.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. 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 professor at the University of Münster. Killing and his spouse had entered the Third Order of Franciscans in 1886.In 1878 Killing wrote on space forms in Crelle's Journal 86:72–83. Two years later he wrote on computations in hyperbolic geometry in the same journal. Recounting lectures of Weierstrass, he there introduced the hyperboloid model described by Weierstrass coordinates.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.From 1888 to 1890, Killing essentially classified the complex finite-dimensional simple Lie algebras, as a requisite step of classifying Lie groups, inventing the notions of a Cartan subalgebra and the Cartan matrix. He thus arrived at the conclusion that, basically, the only simple Lie algebras were those associated to the linear, orthogonal, and symplectic groups, apart from a small number of isolated exceptions. Élie Cartan's 1894 dissertation was essentially a rigorous rewriting of Killing's paper. Killing also introduced the notion of a root system. He discovered the exceptional Lie algebra g2 in 1887; his root system classification showed up all the exceptional cases, but concrete constructions came later.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.\"".
- Wilhelm_Killing award Lobachevsky_Prize.
- Wilhelm_Killing birthDate "1847-05-10".
- Wilhelm_Killing birthPlace Arnsberg_(region).
- Wilhelm_Killing birthPlace Burbach,_North_Rhine-Westphalia.
- Wilhelm_Killing birthPlace Province_of_Westphalia.
- Wilhelm_Killing birthPlace Siegen_district.
- Wilhelm_Killing citizenship Germany.
- Wilhelm_Killing deathDate "1923-02-11".
- Wilhelm_Killing deathPlace Münster.
- Wilhelm_Killing deathPlace Münster_(region).
- Wilhelm_Killing deathPlace Province_of_Westphalia.
- Wilhelm_Killing doctoralAdvisor Ernst_Kummer.
- Wilhelm_Killing doctoralAdvisor Karl_Weierstrass.
- Wilhelm_Killing knownFor Lie_algebra.
- Wilhelm_Killing knownFor Lie_group.
- Wilhelm_Killing knownFor Non-Euclidean_geometry.
- Wilhelm_Killing thumbnail Wilhelm_Karl_Joseph_Killing.jpeg?width=300.
- Wilhelm_Killing wikiPageID "1531824".
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- Wilhelm_Killing wikiPageRevisionID "668433732".
- Wilhelm_Killing wikiPageWikiLink Arnsberg_(region).
- Wilhelm_Killing wikiPageWikiLink Braniewo.
- Wilhelm_Killing wikiPageWikiLink Burbach,_North_Rhine-Westphalia.
- Wilhelm_Killing wikiPageWikiLink Cartan_matrix.
- Wilhelm_Killing wikiPageWikiLink Cartan_subalgebra.
- Wilhelm_Killing wikiPageWikiLink Category:1847_births.
- Wilhelm_Killing wikiPageWikiLink Category:1923_deaths.
- Wilhelm_Killing wikiPageWikiLink Category:19th-century_German_mathematicians.
- Wilhelm_Killing wikiPageWikiLink Category:20th-century_German_mathematicians.
- Wilhelm_Killing wikiPageWikiLink Category:University_of_Münster_faculty.
- Wilhelm_Killing wikiPageWikiLink Collegium_Hosianum.
- Wilhelm_Killing wikiPageWikiLink Coxeter_group.
- Wilhelm_Killing wikiPageWikiLink Crelles_Journal.
- Wilhelm_Killing wikiPageWikiLink Ernst_Kummer.
- Wilhelm_Killing wikiPageWikiLink G2_(mathematics).
- Wilhelm_Killing wikiPageWikiLink Germany.
- Wilhelm_Killing wikiPageWikiLink Harold_Scott_MacDonald_Coxeter.
- Wilhelm_Killing wikiPageWikiLink Hyperbolic_geometry.
- Wilhelm_Killing wikiPageWikiLink Hyperboloid_model.
- Wilhelm_Killing wikiPageWikiLink Karl_Weierstrass.
- Wilhelm_Killing wikiPageWikiLink Killing_form.
- Wilhelm_Killing wikiPageWikiLink Killing_horizon.
- Wilhelm_Killing wikiPageWikiLink Killing_spinor.
- Wilhelm_Killing wikiPageWikiLink Killing_tensor.
- Wilhelm_Killing wikiPageWikiLink Killing_vector_field.
- Wilhelm_Killing wikiPageWikiLink Killing–Hopf_theorem.
- Wilhelm_Killing wikiPageWikiLink Lie_algebra.
- Wilhelm_Killing wikiPageWikiLink Lie_group.
- Wilhelm_Killing wikiPageWikiLink Lobachevsky_Prize.
- Wilhelm_Killing wikiPageWikiLink Mathematician.
- Wilhelm_Killing wikiPageWikiLink Mathematische_Annalen.
- Wilhelm_Killing wikiPageWikiLink Münster.
- Wilhelm_Killing wikiPageWikiLink Münster_(region).
- Wilhelm_Killing wikiPageWikiLink Non-Euclidean_geometry.
- Wilhelm_Killing wikiPageWikiLink Province_of_Westphalia.
- Wilhelm_Killing wikiPageWikiLink Root_system.
- Wilhelm_Killing wikiPageWikiLink Siegen.
- Wilhelm_Killing wikiPageWikiLink Siegen_district.
- Wilhelm_Killing wikiPageWikiLink Simple_Lie_group.
- Wilhelm_Killing wikiPageWikiLink Sophus_Lie.
- Wilhelm_Killing wikiPageWikiLink Space_form.
- Wilhelm_Killing wikiPageWikiLink The_Mathematical_Intelligencer.
- Wilhelm_Killing wikiPageWikiLink Third_Order_of_Saint_Francis.
- Wilhelm_Killing wikiPageWikiLink University_of_Münster.
- Wilhelm_Killing wikiPageWikiLink Weyl_group.
- Wilhelm_Killing wikiPageWikiLink Élie_Cartan.
- Wilhelm_Killing wikiPageWikiLinkText "Killing".
- Wilhelm_Killing wikiPageWikiLinkText "Killing, Wilhelm".
- Wilhelm_Killing wikiPageWikiLinkText "Wilhelm Killing".
- Wilhelm_Killing birthDate "1847-05-10".
- Wilhelm_Killing birthPlace "Burbach near Siegen, Siegen district, Arnsberg, Province of Westphalia".
- Wilhelm_Killing citizenship Germany.
- Wilhelm_Killing deathDate "1923-02-11".
- Wilhelm_Killing deathPlace Münster.
- Wilhelm_Killing deathPlace Münster_(region).
- Wilhelm_Killing deathPlace Province_of_Westphalia.
- Wilhelm_Killing doctoralAdvisor Karl_Weierstrass.
- Wilhelm_Killing doctoralAdvisor "Ernst Kummer".
- Wilhelm_Killing field "Mathematics".
- Wilhelm_Killing knownFor "Lie algebras, Lie groups,".
- Wilhelm_Killing knownFor "and non-Euclidean geometry".
- Wilhelm_Killing name "Wilhelm Karl Joseph Killing".
- Wilhelm_Killing prizes "Lobachevsky Prize".
- Wilhelm_Killing residence "Germany".
- Wilhelm_Killing wikiPageUsesTemplate Template:Authority_control.
- Wilhelm_Killing wikiPageUsesTemplate Template:Citation_needed.
- Wilhelm_Killing wikiPageUsesTemplate Template:DOI.
- Wilhelm_Killing wikiPageUsesTemplate Template:Infobox_scientist.
- Wilhelm_Killing wikiPageUsesTemplate Template:MacTutor_Biography.
- Wilhelm_Killing wikiPageUsesTemplate Template:MathGenealogy.
- Wilhelm_Killing subject Category:1847_births.
- Wilhelm_Killing subject Category:1923_deaths.
- Wilhelm_Killing subject Category:19th-century_German_mathematicians.
- Wilhelm_Killing subject Category:20th-century_German_mathematicians.
- Wilhelm_Killing subject Category:University_of_Münster_faculty.
- Wilhelm_Killing hypernym Mathematician.
- Wilhelm_Killing type Agent.
- Wilhelm_Killing type Person.