Tagged Questions
7
votes
0answers
78 views
Trivial summand of a representation's symmetric power
The following comes from Exercise 13.17 of Fulton and Harris's book, Representation Theory: A First Course.
Let $V$ denote the standard representation of $\mathfrak{sl}_3\mathbb{C}$, with weights ...
0
votes
0answers
26 views
centroid of fixed points
Kindly asking for any hints about the following questions:
Assume that $Γ$ is a finite group, acting on an affine scheme $X$ and a (finite-dimensional) Lie algebra $g$ by automorphisms. We abbreviate ...
0
votes
0answers
44 views
Map algebras between scheme and Lie algebra
Kindly asking for any hints about the following questions:
Suppose, $X$ be an arbitrary scheme over an algebraically closed field $k$.
1- In general, what is the structure of $A= ...
0
votes
0answers
50 views
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 ...
0
votes
0answers
43 views
finite-dimensional Lie algebrab as an scheme
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 ...
2
votes
1answer
117 views
$GL_n(k)$ (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} ...
