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13h
comment cohomology homomorphism induced by classifying map
Usually copying here problems verbatim from textbooks or problem sheets is not very well received... Tell us what you have tried, what you know about the problems, where the problems come from, and so on.
16h
comment How to find the multiplicity of weight in a Verma module?
If you look at the definition of the module, you''ll notice thatit is the number of ways of writing the weight you want as a sum of simple roots.
16h
comment Intermediate field extensions and Degree of field extension
Urgh. The fraction is wrong. Ill fix it later...
19h
comment Intermediate field extensions and Degree of field extension
@SwapnilTripathi, that is not the number of subgroups of a group of order $n$ ---it does work if $G$ is cyclic, though.
19h
answered Intermediate field extensions and Degree of field extension
20h
comment Intermediate field extensions and Degree of field extension
@AndrewBrick, my comment quite directly implies that that is not the case. Forma trivial example, consider an extension of prime degree.
21h
comment Intermediate field extensions and Degree of field extension
In the case of finite Galois extensions, your question is equivalent (since every finite group is the Galois group of some extension) to: is there a relationship between the number of subgroups of a finite group and the number of elements of the group? Considering groups of order $p^n$ with $p$ prime shows that these two numbers do not determine each other.
1d
comment Roots of different irreducible polynomials are algebraically independent
For (1), it obviously depends. I do not believe you cannot find examples...
2d
comment Is the zero matrix diagonalizable?
I am sorry but is there a point to this?
2d
comment Is the zero matrix diagonalizable?
The body should be self-contained.
2d
comment Computing homomorphisms between extensions of modules
I'd rather you played with it for a while first.
2d
comment Is the zero matrix diagonalizable?
By the way: please do not ask your question in the title: the body should be a complete question (and in this case it isn't)
2d
comment Is the zero matrix diagonalizable?
Of course you can say what you wrote in the body of the question, as the left hand side of that equality is evidently the zero matrix.
2d
comment Computing homomorphisms between extensions of modules
It contains a copy of $\hom_R(M_1,N_0)$, and it can be reduced to that.
2d
comment Solvability of ${\rm GL}_2(\mathbb{C})/\mu_n$.
A rather simpler argument shows that it contains a perfect group.
2d
comment Show that $f:V\to W$ is a $(1,1)$-tensor
You should provide us with the definition of what being a tensor is.
2d
comment How to understand $d^2=0$ in differential form?
@Surb, in contexts in which $d$ is discussed, functions are usually infinitely smooth...
Nov
24
comment Compute the map $H^*(CP^n; \mathbb{Z}) \rightarrow H^*(CP^n, \mathbb{Z})$
I think you should talk in person to someone. This is way to messy to explain.
Nov
24
comment Compute the map $H^*(CP^n; \mathbb{Z}) \rightarrow H^*(CP^n, \mathbb{Z})$
Well, those Z are certain relative chomology groups coming from the cw structure. If you trace the whole computation, you can be very explicit about a generator.
Nov
24
comment Compute the map $H^*(CP^n; \mathbb{Z}) \rightarrow H^*(CP^n, \mathbb{Z})$
And how did you compute that? When you did that, you must have exhibited a generator of $H^2$ is one way or another.