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- Kleinian_group abstract "In mathematics, a Kleinian group is a discrete subgroup of PSL(2, C). The group PSL(2, C) of 2 by 2 complex matrices of determinant 1 modulo its center has several natural representations: as conformal transformations of the Riemann sphere, and as orientation-preserving isometries of 3-dimensional hyperbolic space H3, and as orientation preserving conformal maps of the open unit ball B3 in R3 to itself. Therefore a Kleinian group can be regarded as a discrete subgroup acting on one of these spaces. There are some variations of the definition of a Kleinian group: sometimes Kleinian groups are allowed to be subgroups of PSL(2, C).2 (PSL(2, C) extended by complex conjugations), in other words to have orientation reversing elements, and sometimes they are assumed to be finitely generated, and sometimes they are required to act properly discontinuously on a non-empty open subset of the Riemann sphere. A Kleinian group is said to be of type 1 if the limit set is the whole Riemann sphere, and of type 2 otherwise. The theory of general Kleinian groups was founded by Felix Klein (1883) and Henri Poincaré (1883), who named them after Felix Klein. The special case of Schottky groups had been studied a few years before by Schottky.".
- Kleinian_group thumbnail Apollonian_gasket.svg?width=300.
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- Kleinian_group wikiPageExternalLink vorlesungenber01fricuoft.
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- Kleinian_group wikiPageExternalLink index.html.
- Kleinian_group wikiPageID "1362652".
- Kleinian_group wikiPageRevisionID "597896662".
- Kleinian_group authorlink "Felix Klein".
- Kleinian_group authorlink "Henri Poincaré".
- Kleinian_group first "Felix".
- Kleinian_group first "Henri".
- Kleinian_group first "S.L.".
- Kleinian_group hasPhotoCollection Kleinian_group.
- Kleinian_group id "K/k055520".
- Kleinian_group last "Klein".
- Kleinian_group last "Krushkal".
- Kleinian_group last "Poincaré".
- Kleinian_group year "1883".
- Kleinian_group subject Category:3-manifolds.
- Kleinian_group subject Category:Automorphic_forms.
- Kleinian_group subject Category:Discrete_groups.
- Kleinian_group subject Category:Kleinian_groups.
- Kleinian_group subject Category:Lie_groups.
- Kleinian_group type Abstraction100002137.
- Kleinian_group type AutomorphicForms.
- Kleinian_group type DiscreteGroups.
- Kleinian_group type Form106290637.
- Kleinian_group type Group100031264.
- Kleinian_group type KleinianGroups.
- Kleinian_group type LanguageUnit106284225.
- Kleinian_group type LieGroups.
- Kleinian_group type Part113809207.
- Kleinian_group type Relation100031921.
- Kleinian_group type Word106286395.
- Kleinian_group comment "In mathematics, a Kleinian group is a discrete subgroup of PSL(2, C). The group PSL(2, C) of 2 by 2 complex matrices of determinant 1 modulo its center has several natural representations: as conformal transformations of the Riemann sphere, and as orientation-preserving isometries of 3-dimensional hyperbolic space H3, and as orientation preserving conformal maps of the open unit ball B3 in R3 to itself.".
- Kleinian_group label "Kleinian group".
- Kleinian_group label "Kleinsche Gruppe".
- Kleinian_group label "Группа Клейна".
- Kleinian_group label "زمرة كلاينية".
- Kleinian_group sameAs Kleinsche_Gruppe.
- Kleinian_group sameAs m.04wsk3.
- Kleinian_group sameAs Q4116484.
- Kleinian_group sameAs Q4116484.
- Kleinian_group sameAs Kleinian_group.
- Kleinian_group wasDerivedFrom Kleinian_group?oldid=597896662.
- Kleinian_group depiction Apollonian_gasket.svg.
- Kleinian_group isPrimaryTopicOf Kleinian_group.