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In hyperbolic geometry, the Klein quartic, named after Felix Klein, is a compact Riemann surface of genus 3 with the highest possible order automorphism group for this genus, namely order 168 orientation-preserving automorphisms, and 168 × 2 = 336 automorphisms if orientation may be reversed. As such, the Klein quartic is the Hurwitz surface of lowest possible genus; see Hurwitz's automorphisms theorem. Its (orientation-preserving) automorphism group is isomorphic to PSL(2, 7), the second-smallest non-abelian simple group after the alternating group A5. The quartic was first described in.

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rdf:type	bone yago:Artifact100021939 yago:Object100002684 yago:PhysicalEntity100001930 yago:Surface104362025 yago:Whole100003553 yago:WikicatRiemannSurfaces
rdfs:label	Kleinsche Quartik (de) Quartique de Klein (fr) Klein quartic (en) 클라인 4차 곡선 (ko) Quártica Klein (pt)
rdfs:comment	En géométrie hyperbolique, la quartique de Klein, du nom du mathématicien allemand Felix Klein, est une surface de Riemann compacte de genre 3. Elle a le groupe d'automorphismes d'ordre le plus élevé possible parmi les surfaces de Riemann de genre 3, à savoir le groupe simple d'ordre 168. La quartique de Klein est en conséquence la (en) de genre le plus bas possible. (fr) 대수기하학에서 클라인 4차 곡선(Klein4次曲線, 영어: Klein’s quartic curve)은 종수 3의 리만 곡면 가운데 가장 대칭적인 것인 모듈러 곡선이다. (ko) Die Kleinsche Quartik ist eine Kurve 4. Grades in der komplexen projektiven Ebene, die in homogenen Koordinaten durch die Gleichung gegeben ist. Sie wurde 1879 durch Felix Klein eingeführt und besitzt außergewöhnliche Symmetrieeigenschaften. Der algebraischen Kurve entspricht eine Riemannsche Fläche. Betrachtet man die hyperbolische Ebene als komplexe obere Halbebene , auf der wirkt, so ist die Riemannsche Fläche zur Klein-Quartik gegeben durch mit der Kongruenzuntergruppe Sie ist eine Modulkurve (mit Geschlecht 3 und 24 Spitzen, siehe Modulform). (de) In hyperbolic geometry, the Klein quartic, named after Felix Klein, is a compact Riemann surface of genus 3 with the highest possible order automorphism group for this genus, namely order 168 orientation-preserving automorphisms, and 168 × 2 = 336 automorphisms if orientation may be reversed. As such, the Klein quartic is the Hurwitz surface of lowest possible genus; see Hurwitz's automorphisms theorem. Its (orientation-preserving) automorphism group is isomorphic to PSL(2, 7), the second-smallest non-abelian simple group after the alternating group A5. The quartic was first described in. (en) Na geometria hiperbólica, a quártica Klein (nomeado por Felix Klein) é uma superfície de Riemann compacta do gênero 3 com o grupo de automorfismo de ordem mais alta possível para esse gênero, com ordem de 168 automorfismos de preservação de orientação e 336 automorfismos se a orientação puder ser revertida. Como tal, o quártico Klein é a do gênero mais baixo possível; veja . Seu grupo de automorfismo (preservação da orientação) é isomórfico ao , o segundo menos grupo simples não-abeliano. O quártico foi primeiramente descrito em por Klein, em 1878. (pt)
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Wikipage revision ID	1119047521 (xsd:integer)
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