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About: Fuchsian group     Goto   Sponge   NotDistinct   Permalink

An Entity of Type : yago:WikicatFractals, within Data Space : dbpedia.demo.openlinksw.com associated with source document(s)

Type: Thingyago:Abstraction100002137yago:Cognition100023271yago:Form105930736yago:Fractal105931152yago:Group100031264yago:PsychologicalFeature100023100yago:WikicatKleinianGroupsethnic groupyago:Structure105726345yago:WikicatDiscreteGroupsyago:WikicatFractals New Facet based on Instances of this Class

In mathematics, a Fuchsian group is a discrete subgroup of PSL(2,R). The group PSL(2,R) can be regarded equivalently as a group of isometries of the hyperbolic plane, or conformal transformations of the unit disc, or conformal transformations of the upper half plane, so a Fuchsian group can be regarded as a group acting on any of these spaces. There are some variations of the definition: sometimes the Fuchsian group is assumed to be finitely generated, sometimes it is allowed to be a subgroup of PGL(2,R) (so that it contains orientation-reversing elements), and sometimes it is allowed to be a Kleinian group (a discrete subgroup of PSL(2,C)) which is conjugate to a subgroup of PSL(2,R).