# Integral forms of loop algebras.

The question following is about integral forms for semisimple Lie algebras and loop algebras constructed from them.

Let $\frak g$ a finite-dimensional Lie algebra over $\mathbb C$ and $L(\frak g)=\frak g \otimes \mathbb C[t,t^{-1}]$ its loop algebra. Kostant's form offers an integral form to $\frak g$ and Garland's form offers one to $L(\frak g)$.

Let $I$ be an ideal of $L(\frak g)$. Consider $U_\mathbb Z(L(\frak g))$ an integral form of $L(\frak g)$.

Does exists an integral form of $\frac{L(\frak g)}{I}$? If yes, is there a relation between this integral form and an integral form of $U_\mathbb Z(L(\frak g))$?

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