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Let $\mathfrak{g}$ be a simple lie algebra over $\mathbb{C}$. Let $Rep(\mathfrak{g})$ denote the category of finite dimensional $\mathfrak{g}$-modules. For every $V \in Rep(\mathfrak{g})$ define $Rep_ …

This is inevitably an imprecise question, but there are already several questions like this on the site so I thought i'd try anyway. If I understand correctly, for any reductive algebraic group $G$ th …

Let $X$ be a projective algebraic variety over a (perfect) field $k$. Let $Aut(X):k \text{-}Alg \to Grp$ be the functor of points defined by $$Aut(X) : A \mapsto Aut_{Spec (A)}(X \times_{k} Spec …

Algebraic groups are very rich objects. As such, a large bag of examples against which one can test his intuition can be very helpful in learning the general theory. What are some good didactic (coun …

I believe there has been at least one question similar to this one and yet I still think this particular question deserves to have a thread of its own. I'm becoming increasingly fascinated by stuff r …