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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).

Referenced By

This article is licensed under the GNU Free Documentation License. It uses material from the Wikipedia article "Upper half plane".