Meta tags:

Headings (most frequently used words):

edit, navigation, tools, wilhelm, killing, contents, life, work, selected, works, see, also, references, external, links, menu, personal, namespaces, views, search, contribute, print, export, in, other, projects, languages,

Text of the page (most frequently used words):
#killing (42), the (31), with (20), articles (18), and (15), lie (15), die (15), identifiers (14), was (12), edit (9), doi (9), der (9), wikipedia (8), s2cid (8), 1007 (8), mathematische (8), annalen (8), from (7), geometry (7), groups (7), wilhelm (6), transformationsgruppen (6), journal (6), non (5), all (5), university (5), münster (5), german (5), endlichen (5), work (5), raumformen (5), that (5), algebras (5), his (5), about (4), terms (4), may (4), this (4), commons (4), page (4), links (4), 1923 (4), mathematics (4), hyperbolic (4), also (4), 1890 (4), zusammensetzung (4), stetigen (4), geometrie (4), für (4), reine (4), und (4), angewandte (4), mathematik (4), 1885 (4), euclidean (4), weierstrass (4), karl (4), wikimedia (3), wikidata (3), article (3), navigation (3), history (3), 1847 (3), org (3), mathematician (3), mathematical (3), root (3), system (3), theil (3), grundlagen (3), ueber (3), nicht (3), euklidischen (3), 1880 (3), later (3), cartan (3), had (3), transformations (3), became (3), professor (3), view (2), contact (2), privacy (2), policy (2), under (2), using (2), 2022 (2), other (2), information (2), link (2), pages (2), upload (2), file (2), related (2), changes (2), tools (2), contents (2), search (2), talk (2), contributions (2), not (2), categories (2), sudoc (2), zbmath (2), viaf (2), isni (2), unsourced (2), statements (2), short (2), description (2), siegen (2), century (2), mathematicians (2), https (2), wilhelm_killing (2), scientific (2), germany (2), archive (2), john (2), external (2), coleman (2), paper (2), new (2), york (2), isbn (2), 1993 (2), hyperboloid (2), references (2), equation (2), see (2), von (2), 1889 (2), 1888 (2), transformation (2), paderborn (2), schöningh (2), einführung (2), 1893 (2), 1892 (2), den (2), 1878 (2), selected (2), works (2), weyl (2), years (2), orders (2), born (2), coxeter (2), essentially (2), simple (2), were (2), number (2), dissertation (2), rigorous (2), introduced (2), classification (2), exceptional (2), but (2), which (2), out (2), goals (2), made (2), wrote (2), further (2), lorentz (2), 1872 (2), college (2), order (2), ernst (2), kummer (2), life (2), february (2), joseph (2), province (2), westphalia (2), jump (2), web (2), sep (2), cookie, statement, statistics, developers, mobile, disclaimers, text, available, additional, apply, site, you, agree, registered, trademark, profit, organization, foundation, inc, use, creative, attribution, sharealike, license, last, edited, october, utc, svenska, русский, português, polski, nederlands, مصرى, मराठी, kreyòl, ayisyen, עברית, italiano, interlingua, bahasa, indonesia, 한국어, français, فارسی, español, deutsch, čeština, català, تۆرکجه, العربية, languages, projects, printable, version, download, pdf, print, export, item, cite, permanent, special, what, here, recent, community, portal, learn, help, contribute, donate, random, current, events, main, more, read, views, english, namespaces, log, create, account, logged, personal, menu, hidden, fast, mgp, dtbio, nta, nkc, lccn, j9u, gnd, bibsys, worldcatid, category, 2013, infobox, scientist, unknown, parameters, hcards, matches, people, wittgenstein, faculty, deaths, births, 20th, 19th, retrieved, index, php, title, oldid, 1117751385, france, faceted, application, subject, terminology, genealogy, project, databases, biographical, dictionaries, netherlands, czech, republic, united, states, israel, norway, national, libraries, worldcat, general, authority, control, media, andrews, mactutor, robertson, edmund, connor, greatest, time, vol, intelligencer, ratcliffe, 1994, 038794348x, 104, foundations, manifolds, reynolds, 442, 455, 2324297, jstor, 1080, 00029890, 11990430, 100, american, monthly, hawkins, thomas, 2000, springer, 387, 98963, emergence, theory, levi, decomposition, vector, field, tensor, spinor, horizon, hopf, theorem, form, 239, 254, 121548146, bf01207841, bestimmung, grössten, untergruppen, 161, 189, 179178061, bf01207837, vierter, 423, 432, 121050972, bf01443863, erweiterung, des, begriffes, invarianten, 122, 179177899, bf01446792, dritter, 124198118, bf01444109, zweiter, 252, 290, 120501356, bf01211904, 1898, 1897, 569, 590, 121748880, bf01446454, zur, projectiven, 121, 186, 109, 1891, 257, 278, 119473479, bf01206655, clifford, klein, schen, leipzig, teubner, 1884, mechanik, 1879, 265, 287, rechnung, 1877, zwei, mit, constanter, positiver, krümmung, says, exhibited, characteristic, when, old, listed, before, group, classified, complex, finite, dimensional, requisite, step, classifying, inventing, notions, thus, arrived, conclusion, basically, only, those, associated, linear, orthogonal, symplectic, apart, small, isolated, exceptions, 1894, rewriting, notion, discovered, 1887, showed, cases, concrete, constructions, came, algebra, élie, matrix, subalgebra, invented, independently, around, library, did, contain, scandinavian, appeared, scornful, perhaps, competitive, spirit, claimed, valid, already, been, proven, invalid, added, fact, less, logically, than, much, grander, unproven, conjectures, turned, true, because, high, excessively, modest, own, achievement, citation, needed, sophus, developed, well, recounting, lectures, there, described, credited, formulating, mathematically, equivalent, dimensions, coordinates, model, crelle, space, forms, studied, berlin, taught, gymnasia, secondary, schools, 1868, seminary, braunsberg, now, took, holy, take, teaching, position, rector, chair, town, council, administrator, widely, liked, respected, finally, spouse, entered, 1886, third, franciscans, braniewo, collegium, hosianum, who, important, theories, doctoral, advisor, fields, career, 1900, lobachevsky, prize, awards, known, for, citizenship, aged, died, near, arnsberg, siegerland, burbach, free, encyclopedia, wayback, machine, http, 20221028052858, wiki, timestamps, capture, fail, success, 2023, 2021, nov, oct, 2006, jul, 2026, 120, captures,

Text of the page (random words):
wilhelm killing wikipedia 120 captures 13 sep 2006 13 jul 2026 sep oct nov 28 2021 2022 2023 success fail about this capture timestamps the wayback machine http web archive org web 20221028052858 https en wikipedia org wiki wilhelm_killing wilhelm killing from wikipedia the free encyclopedia jump to navigation jump to search german mathematician wilhelm karl joseph killing born 10 may 1847 burbach near siegen siegerland arnsberg province of westphalia died 11 february 1923 1923 02 12 aged 75 münster münster province of westphalia citizenship german known for lie algebras lie groups and non euclidean geometry 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 contents 1 life 2 work 3 selected works 4 see also 5 references 6 external links life edit 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 work edit further information history of lorentz transformations in 1878 killing wrote on space forms in terms of non euclidean geometry in crelle s journal which he further developed in 1880 as well as in 1885 1 recounting lectures of weierstrass he there introduced the hyperboloid model of hyperbolic geometry described by weierstrass coordinates 2 he is also credited with formulating transformations mathematically equivalent to lorentz transformations in n dimensions in 1885 3 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 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 g 2 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 4 selected works edit 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 doi 10 1007 bf01206655 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 doi 10 1007 bf01446454 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 doi 10 1007 bf01211904 s2cid 120501356 killing w 1889 die zusammensetzung der stetigen endlichen transformationsgruppen zweiter theil mathematische annalen 33 1 48 doi 10 1007 bf01444109 s2cid 124198118 killing w 1889 die zusammensetzung der stetigen endlichen transformationsgruppen dritter theil mathematische annalen 34 57 122 doi 10 1007 bf01446792 s2cid 179177899 killing w 1890 erweiterung des begriffes der invarianten von transformationsgruppen mathematische annalen 35 3 423 432 doi 10 1007 bf01443863 s2cid 121050972 killing w 1890 die zusammensetzung der stetigen endlichen transformationsgruppen vierter theil mathematische annalen 36 161 189 doi 10 1007 bf01207837 s2cid 179178061 killing w 1890 bestimmung der grössten untergruppen von endlichen transformationsgruppen mathematische annalen 36 239 254 doi 10 1007 bf01207841 s2cid 121548146 see also edit killing equation killing form killing hopf theorem killing horizon killing spinor killing tensor killing vector field levi decomposition g2 mathematics root system references edit hawkins thomas 2000 emergence of the theory of lie groups new york springer isbn 0 387 98963 3 reynolds w f 1993 hyperbolic geometry on a hyperboloid the american mathematical monthly 100 5 442 455 doi 10 1080 00029890 1993 11990430 jstor 2324297 ratcliffe j g 1994 hyperbolic geometry foundations of hyperbolic manifolds new york pp 56 104 isbn 038794348x coleman a john the greatest mathematical paper of all time the mathematical intelligencer vol 11 no 3 pp 29 38 external links edit 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 authority control general isni 1 viaf 1 worldcat national libraries norway germany israel united states czech republic netherlands biographical dictionaries germany scientific databases mathematics genealogy project zbmath other faceted application of subject terminology sudoc france 1 retrieved from https en wikipedia org w index php title wilhelm_killing oldid 1117751385 categories 19th century german mathematicians 20th century german mathematicians 1847 births 1923 deaths university of münster faculty people from siegen wittgenstein hidden categories articles with short description short description matches wikidata articles with hcards pages using infobox scientist with unknown parameters all articles with unsourced statements articles with unsourced statements from may 2013 commons category link is on wikidata articles with isni identifiers articles with viaf identifiers articles with worldcatid identifiers articles with bibsys identifiers articles with gnd identifiers articles with j9u identifiers articles with lccn identifiers articles with nkc identifiers articles with nta identifiers articles with dtbio identifiers articles with mgp identifiers articles with zbmath identifiers articles with fast identifiers articles with sudoc identifiers navigation menu personal tools not logged in talk contributions create account log in namespaces article talk english views read edit view history more search navigation main page contents current events random article about wikipedia contact us donate contribute help learn to edit community portal recent changes upload file tools what links here related changes upload file special pages permanent link page information cite this page wikidata item print export download as pdf printable version in other projects wikimedia commons languages العربية تۆرکجه català čeština deutsch español فارسی français 한국어 bahasa indonesia interlingua italiano עברית kreyòl ayisyen मराठी مصرى nederlands polski português русский svenska 中文 edit links this page was last edited on 23 october 2022 at 11 10 utc text is available under the creative commons attribution sharealike license 3 0 additional terms may apply by using this site you agree to the terms of use and privacy policy wikipedia is a registered trademark of the wikimedia foundation inc a non profit organization privacy policy about wikipedia disclaimers contact wikipedia mobile view developers statistics cookie statement