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. 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

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  • Wilhelm Killing (* 10. Mai 1847 in Burbach bei Siegen; † 11. Februar 1923 in Münster) war ein deutscher Mathematiker. (de)
  • 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. 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." (en)
  • Killing studiò all'università di Münster e nel 1872 fu autore di una dissertazione sotto la guida Karl Weierstrass e Ernst Kummer a Berlino nel 1872. Iniziò la sua carriera cattedratica al "Collegium Hosianum" di Braniewo, dove peraltro in seguito assunse la posizione di rettore. Nel 1886 entrò a far parte del "Terzo ordine francescano" (it)
  • Wilhelm Karl Joseph Killing (10 mai 1847 – 11 février 1923) est un mathématicien allemand connu pour ses nombreuses contributions aux théories des algèbres de Lie et des groupes de Lie et à la géométrie non euclidienne. (fr)
  • Wilhelm Karl Joseph Killing (Burbach, 10 mei 1847 - Münster, 11 februari 1923) was een Duits wiskundige, die belangrijke bijdragen heeft geleverd aan de Lie-algebra, Lie-groep en niet-euclidische meetkunde. Hij heeft gestudeerd aan de Universiteit van Münster en later schreef hij zijn proefschrift in Berlijn in 1872. Hij gaf les in het gymnasium van 1868 tot 1872. Hij werd professor aan het seminarie-college in Braumsberg (nu Braniewo). Hij nam belangrijke beslissingen om een leraarpositie te krijgen. Hij werd rector op het college en leider van de stadsraad. Hij was een gewaardeerd professor, en in 1892 werd hij professor aan de Universiteit van Münster. (nl)
  • Wilhelm Karl Joseph Killing (ur. 10 maja 1847 w Burbach w Nadrenii Północnej-Westfalii, zm. 11 lutego 1923 w Münster) – niemiecki matematyk, autor istotnych prac z zakresu teorii algebr i grup Liego oraz geometrii nieeuklidesowej. (pl)
  • Wilhelm Karl Joseph Killing (Burbach, Vestfália, 10 de maio de 1847 — Münster, 11 de fevereiro de 1923) foi um matemático alemão. (pt)
  • 威廉·卡尔·约瑟夫·基灵(Wilhelm Karl Joseph Killing,1847年4月10日-1923年2月11日)是一个德国数学家,在李代数、李群与非欧几里得几何等理论作出了重要贡献。 基灵就读于明斯特大学,随后1872年在卡尔·魏尔斯特拉斯与恩斯特·库默尔的指导下在柏林写博士论文。他从1868年到1872年在中学教书。他成为布劳恩斯贝格(现在的布拉涅沃)的神学院 Collegium Hosianum 一名教授。为了获得教职他成为牧师,并当上院长以及镇议会的主席。作为教授和管理者基灵广受爱戴和尊重。最后,在1892年他成为明斯特大学的教授。基灵和他的夫人在1886年进入方济各会第三会(Third Order)。 基灵独立于索菲斯·李大约在1880年发现了李代数。基灵的大学图书馆没有刊登李的文章的斯堪的纳维亚杂志(李后来嘲笑基灵,有点脱离了竞争精神,声称所有有价值的已经由李证明了,而所有基灵添加的都是无价值的)。事实上基灵工作的逻辑严密性要逊于李,但基灵有对群分类的更宏伟的目标,并作出了许多未经证明的而确实正确的猜想。因为基灵的目标如此之高,他对自己的成就过于谦虚。 基灵在1888年至1890年间本质上将复单李代数分类,发明了嘉当子代数和嘉当矩阵概念。埃利·嘉当的博士论文本质上对基灵的文章的严格化重写。基灵也引入了根系概念。他在1887年发现了例外李代数 g2;他的根系分类指出了所有例外情形,但实例到后来才发现。 如 A. J. 科尔曼所说:“当外尔三岁时,他展示了外尔群的特征方程;在考克斯特出生19年前列出了考克斯特变换的阶数。” 基灵还对矩阵引入了特征方程。 (zh)
  • Вильгельм Карл Йозеф Киллинг (нем. Wilhelm Karl Joseph Killing; 10 мая 1847, Бурбах (Зигерланд) — 11 февраля 1923, Мюнстер, Германия) — немецкий математик, который сделал важный вклад в теории алгебр Ли, групп Ли и неевклидову геометрию. (ru)
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  • German mathematician (en)
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http://purl.org/linguistics/gold/hypernym
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rdfs:comment
  • Wilhelm Killing (* 10. Mai 1847 in Burbach bei Siegen; † 11. Februar 1923 in Münster) war ein deutscher Mathematiker. (de)
  • Killing studiò all'università di Münster e nel 1872 fu autore di una dissertazione sotto la guida Karl Weierstrass e Ernst Kummer a Berlino nel 1872. Iniziò la sua carriera cattedratica al "Collegium Hosianum" di Braniewo, dove peraltro in seguito assunse la posizione di rettore. Nel 1886 entrò a far parte del "Terzo ordine francescano" (it)
  • Wilhelm Karl Joseph Killing (10 mai 1847 – 11 février 1923) est un mathématicien allemand connu pour ses nombreuses contributions aux théories des algèbres de Lie et des groupes de Lie et à la géométrie non euclidienne. (fr)
  • Wilhelm Karl Joseph Killing (ur. 10 maja 1847 w Burbach w Nadrenii Północnej-Westfalii, zm. 11 lutego 1923 w Münster) – niemiecki matematyk, autor istotnych prac z zakresu teorii algebr i grup Liego oraz geometrii nieeuklidesowej. (pl)
  • Wilhelm Karl Joseph Killing (Burbach, Vestfália, 10 de maio de 1847 — Münster, 11 de fevereiro de 1923) foi um matemático alemão. (pt)
  • Вильгельм Карл Йозеф Киллинг (нем. Wilhelm Karl Joseph Killing; 10 мая 1847, Бурбах (Зигерланд) — 11 февраля 1923, Мюнстер, Германия) — немецкий математик, который сделал важный вклад в теории алгебр Ли, групп Ли и неевклидову геометрию. (ru)
  • 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. 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 (en)
  • Wilhelm Karl Joseph Killing (Burbach, 10 mei 1847 - Münster, 11 februari 1923) was een Duits wiskundige, die belangrijke bijdragen heeft geleverd aan de Lie-algebra, Lie-groep en niet-euclidische meetkunde. (nl)
  • 威廉·卡尔·约瑟夫·基灵(Wilhelm Karl Joseph Killing,1847年4月10日-1923年2月11日)是一个德国数学家,在李代数、李群与非欧几里得几何等理论作出了重要贡献。 基灵就读于明斯特大学,随后1872年在卡尔·魏尔斯特拉斯与恩斯特·库默尔的指导下在柏林写博士论文。他从1868年到1872年在中学教书。他成为布劳恩斯贝格(现在的布拉涅沃)的神学院 Collegium Hosianum 一名教授。为了获得教职他成为牧师,并当上院长以及镇议会的主席。作为教授和管理者基灵广受爱戴和尊重。最后,在1892年他成为明斯特大学的教授。基灵和他的夫人在1886年进入方济各会第三会(Third Order)。 基灵独立于索菲斯·李大约在1880年发现了李代数。基灵的大学图书馆没有刊登李的文章的斯堪的纳维亚杂志(李后来嘲笑基灵,有点脱离了竞争精神,声称所有有价值的已经由李证明了,而所有基灵添加的都是无价值的)。事实上基灵工作的逻辑严密性要逊于李,但基灵有对群分类的更宏伟的目标,并作出了许多未经证明的而确实正确的猜想。因为基灵的目标如此之高,他对自己的成就过于谦虚。 如 A. J. 科尔曼所说:“当外尔三岁时,他展示了外尔群的特征方程;在考克斯特出生19年前列出了考克斯特变换的阶数。” 基灵还对矩阵引入了特征方程。 (zh)
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  • Wilhelm Killing (de)
  • Wilhelm Killing (en)
  • Wilhelm Killing (it)
  • Wilhelm Killing (fr)
  • Wilhelm Killing (nl)
  • Wilhelm Killing (pl)
  • Wilhelm Killing (pt)
  • Киллинг, Вильгельм (ru)
  • 威廉·基灵 (zh)
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