# Tagged Questions

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### Regular elements of a module is open and dense

Let $\mathfrak{g}$ be an algebraic Lie algebra and $V$ be a $\mathfrak{g}$-module, then for each $v\in V$, define $\mathfrak{g}^v = \{x\in\mathfrak{g}:xv = 0\}$. Let $V_{reg}$ be the set of all $v$ ...
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### Lie algebra homomorphism as an scheme morphism

Kindly asking for any hints about the following questions: Assume $g$ is a finite-dimensional Lie algebra. We denote the group of Lie algebra automorphisms of $g$ by $\rm Aut_k g$. Any Lie algebra ...
Kindly asking for any hints about the following questions: Suppose $k$ is an algebraically closed field of characteristic zero and $g$ is a finite-dimensional Lie algebra over $k$. Then $g$ is ...
### $GL_n(k)$ (General linear group over a algebraically closed field) as a affine variety?
In the context of linar algebraic groups, I read in my notes from the lecture that's already some while ago that $GL_n(k)$ is an algebraic variety because $GL_n=D(\det)$, \$ \det \in k [ (X_{ij})_{i,j} ...