# Reference request: exact sequences of Lie algebras

I have a reference request: where can I read more about the following?

Consider the short exact sequence $0\rightarrow \mathfrak{n}^- \rightarrow \mathfrak{gl}_n\rightarrow \mathfrak{b}\rightarrow 0$, where $\mathfrak{b}$ is a Borel subalgebra in $\mathfrak{gl}_n$. Let $U$ be the maximal unipotent subgroup of $B$, where $B$ is the Lie group corresponding to $\mathfrak{b}$. Let $k$ be an algebraically closed field.

Then there exists a short exact sequence or an exact sequence of the form $$0\rightarrow k[\mathfrak{b}]^U\rightarrow k[\mathfrak{gl}_n]^U\rightarrow k[\mathfrak{n}^-]^U \rightarrow \ldots$$

Will I find more information in a book in Lie groups and Lie algebras or in equivariant cohomology?