The Upper half plane reference article from the English Wikipedia on 24-Apr-2004 (provided by Fixed Reference: snapshots of Wikipedia from wikipedia.org)

Upper half plane

In mathematics, the upper half plane H is the set of complex numbers x+iy such that y>0. It is the domain of many functions of interest in complex analysis, especially modular forms. It is also a model of the hyperbolic plane.

There is a group action of the special linear group SL(2,R) on H defined by

The action is transitive and the stabilizer of i is the rotation group

Therefore, H = SL(2,R)/SO(2).

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