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Consider the group $G = \left\{\begin{pmatrix} a & b\\ 0 & 1\end{pmatrix}: a \in \mathbb{C}^{\times}, b \in \mathbb{C}\right\} \subset GL(2, \mathbb{C})$. How does one find the universal cover of this group? In general, if I had a larger explicit matrix, what would I do?

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    I changed the tags to two that I thought were most specific -- feel free to revert. Interesting question!2012-04-02
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    Do you know how to find the universal cover of $G$ as a topological space, and how to write down the covering map? From there it suffices to figure out how to lift the group structure.2012-04-02
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    Er, no actually, how would I go about doing that?2012-04-02
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    @109230: okay. Do you know how to find the universal cover of $\mathbb{C}^{\times}$?2012-04-03

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