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39/20 answers
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Mar
20
answered For an element $x$ in an algebraic group $G$, why do we have $\mathscr{L}(C_G(x))\subset\mathfrak{c}_{\mathfrak{g}}(x)$?
Mar
14
reviewed Approve How to show that the coordinate ring of a finite set of points in projective space is Cohen-Macaulay?
Mar
13
revised What is the coordinate ring of $G/U$?
added 1330 characters in body
Mar
11
accepted Orthogonal invariants of an irredubile GL-representation
Mar
11
comment Orthogonal invariants of an irredubile GL-representation
The partition corresponding to the invariants should be $(0)$, not $(1)$ - that'd mean that it's the case if $\lambda$ has only even summands, right?
Mar
11
asked Orthogonal invariants of an irredubile GL-representation
Feb
27
accepted Does the quotient of an algebraic group by its neutral component always split?
Feb
27
asked Does the quotient of an algebraic group by its neutral component always split?
Feb
25
reviewed Approve Probability Distribution Function for Nonlinear Function
Feb
25
reviewed Approve Compare the topological spaces?
Feb
24
answered Dimension of a $G$-variety $X$ that is a finite union of $G$-orbits
Feb
23
reviewed Approve For what values of $k$ does this system of equations have a unique solution?
Feb
23
reviewed Approve Representing $-2.5$ as a floating point number
Feb
21
accepted Confusion about the quotient $G/B$
Feb
21
comment Confusion about the quotient $G/B$
Alright. A categorical quotient is defined on wikipedia, and I think the problem is that $\operatorname{Spec}(\C[G]^U)$ is a categorical quotient inside the category of affine varieties, but it is not a categorical quotient in the category of varieties, or even $\C$-schemes.
Feb
21
comment Confusion about the quotient $G/B$
Okay. I think this will help me to get there. @TobiasKildetoft: You were right, the flaw is in my argument that a quotient is affine just because it has a finitely generated ring of rational functions.
Feb
21
comment Confusion about the quotient $G/B$
Hm. I see what you are saying. My line of argument, however, is more like this: I can consider $\operatorname{Spec}(\C[G]^U)$ which is an affine variety. It also seems to be a categorical quotient of $G$ by $U$.
Feb
21
comment Confusion about the quotient $G/B$
But we are talking about affine varieties, and for those kinds of schemes it's true. Just to be clear, though: You say that $G/U$ is not affine, right?
Feb
21
comment Confusion about the quotient $G/B$
I thought that I could take the spectrum of this finitely generated algebra and get an affine, categorical quotient: Since those are unique and geometric quotients are categorical, the statement would follow.
Feb
21
asked Confusion about the quotient $G/B$