Kleinian group

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 H, and as orientation preserving conformal maps of the open unit ball B in R to itself. Therefore a Kleinian group can be regarded as a discrete subgroup acting on one of these spaces.