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YCor
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Tensor algebra and Universaluniversal enveloping algebra

Let $\mathfrak g$ be a Lie algebra which is NOTnot reductive. Let $T(\mathfrak g)$ and $U(\mathfrak g)$ be the tensor algebra and universal enveloping algebra of $\mathfrak g$ respectively. We have a cannonical surjection $p: T(\mathfrak g) \rightarrow U(\mathfrak g)$. Does it give a surjective map from $T(\mathfrak g)^{\mathfrak g}$ to $U(\mathfrak g)^{\mathfrak g}$ ? Here $T(\mathfrak g)^{\mathfrak g}$ (resp. $U(\mathfrak g)^{\mathfrak g}$) are the $\mathfrak g$-invariants of $T(\mathfrak g)$ (resp. $U(\mathfrak g)$).

Tensor algebra and Universal enveloping algebra

Let $\mathfrak g$ be a Lie algebra which is NOT reductive. Let $T(\mathfrak g)$ and $U(\mathfrak g)$ be the tensor algebra and universal enveloping algebra of $\mathfrak g$ respectively. We have a cannonical surjection $p: T(\mathfrak g) \rightarrow U(\mathfrak g)$. Does it give a surjective map from $T(\mathfrak g)^{\mathfrak g}$ to $U(\mathfrak g)^{\mathfrak g}$ ? Here $T(\mathfrak g)^{\mathfrak g}$ (resp. $U(\mathfrak g)^{\mathfrak g}$) are the $\mathfrak g$-invariants of $T(\mathfrak g)$ (resp. $U(\mathfrak g)$).

Tensor algebra and universal enveloping algebra

Let $\mathfrak g$ be a Lie algebra which is not reductive. Let $T(\mathfrak g)$ and $U(\mathfrak g)$ be the tensor algebra and universal enveloping algebra of $\mathfrak g$ respectively. We have a cannonical surjection $p: T(\mathfrak g) \rightarrow U(\mathfrak g)$. Does it give a surjective map from $T(\mathfrak g)^{\mathfrak g}$ to $U(\mathfrak g)^{\mathfrak g}$ ? Here $T(\mathfrak g)^{\mathfrak g}$ (resp. $U(\mathfrak g)^{\mathfrak g}$) are the $\mathfrak g$-invariants of $T(\mathfrak g)$ (resp. $U(\mathfrak g)$).

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Tensor algebra and Universal enveloping algebra

Let $\mathfrak g$ be a Lie algebra which is NOT reductive. Let $T(\mathfrak g)$ and $U(\mathfrak g)$ be the tensor algebra and universal enveloping algebra of $\mathfrak g$ respectively. We have a cannonical surjection $p: T(\mathfrak g) \rightarrow U(\mathfrak g)$. Does it give a surjective map from $T(\mathfrak g)^{\mathfrak g}$ to $U(\mathfrak g)^{\mathfrak g}$ ? Here $T(\mathfrak g)^{\mathfrak g}$ (resp. $U(\mathfrak g)^{\mathfrak g}$) are the $\mathfrak g$-invariants of $T(\mathfrak g)$ (resp. $U(\mathfrak g)$).