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Let $\mathfrak{g}$ be a simple finite-dimensional complex Lie algebra and set by $\tilde{\mathfrak{g}}:=\mathfrak{g}\otimes_{\mathbb C} \mathbb{C}[t,t^{-1}]$ its loop algebra.

How to express the universal enveloping algebra $U(\tilde{\mathfrak{g}})$ of $\tilde{\mathfrak{g}}$ as a quotient $\frac{ A_{X}}{I}$, where $A_{X}$ is a free associative algebra over some set $X$ and $I$ is an ideal of $A_{X}$?

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    @Matt: as I said above, the universal enveloping algebra has a standard presentation you can use in terms of a presentation for $\tilde{\mathfrak{g}}$, and $\tilde{\mathfrak{g}}$ in turn has a reasonable presentation in terms of a presentation of $\mathfrak{g}$.2012-08-19

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