# Generator of translation for the hyperbolic plane? [closed]

What is the generator of translation in the Beltrami-Klein model of the hyperbolic plane?

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I've voted to close. math.stackexchange.com is a more appropriate forum for your question. –  Ryan Budney Jun 2 '11 at 7:05
I've also voted to close. The notion of "the generator of translation" also makes no sense, as r0b0t's answer below suggests. –  José Figueroa-O'Farrill Jun 2 '11 at 13:29
Hyperbolic plane is a homogeneous space $G/H$ where $G$ acts by isometries and so any reasonable defined `translation' is given by the natural left action of $G$. Decide what elements of $G$ will you call translations and then for any abstract generator $X\in\mathfrak{g}$ such that $\exp{tX}$ is translation, compose the natural left action with diffeomorphism of $G/H$ to your favorite model. Differentiate the resulting map at zero and you are done.