Fuchsian groupとは 意味・読み方・使い方

In mathematics, a Fuchsian group is a discrete subgroup of PSL2(R). The group PSL₂(R) can be regarded 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 PGL₂(R) = PSL₂(R).2 (so that it contains orientation-reversing elements) and sometimes it is allowed to be a a Kleinian group (a discrete group of PSL(2,C)) that is conjugate to a subgroup of PSL₂(R).