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2d
comment lattice in number field already a fractional ideal?
You are specifying $f$ at all $x_i\cdot x_j$ which is more than $n$ in number, exceeding the degree of $K$; how can you guarantee such a linear map exists?
2d
comment Variations to Cayley's Embedding Theorem for Groups
@ Derek Holt: Your second paragraph is the interpretation I had in my mind. But the Weyl groups $N(T)/T$ are not subgroups of Lie groups, Only the group $N(T)$ is a subgroup of $G$. Can you clarify?
2d
asked Variations to Cayley's Embedding Theorem for Groups
2d
comment Advice for number theory library
I have heard that L.E. Dickson's century-old work History of the Theory of Numbers in three volumes is a great work. According to Wikepedia this totals to 1600+ pages.
Apr
13
awarded  Yearling
Apr
13
comment Secant Lines contained in Hypersurfaces
+1 for a clear answer.
Apr
12
comment Is the big cell a principal open set?
Is this an intrinsic property? Does not it depend on how the affine algebraic group is realized as a linear algebraic group?
Apr
12
comment How can I solve a cubic equation in a finite field with characteristic 2?
Nice idea; it is amazing that linear algebra can be exploited to solve a cubic equation. Are there any similar tricks in other characteristics , especially 0?
Apr
10
comment Quotient of product of curves
Somewhat tangential: see the work of Guralnick on Beauville structure about obtaining smooth projective surfaces as a quotient by finite group action on product of curves. One link is arxiv.org/abs/1009.6183
Apr
4
comment Counting solutions modulo primes
Sorry, if I sound dumb. What is the meaning of "up to $x$"? As $x$ is a symbolic variable, and this upto $x$ sounds like bounded above by $x$, I am confused.
Mar
29
comment If y forms Pythagorean triples with two different x, can some other y also form Pythagorean triples with those two x?
Under that interpretation my answer gives nothing.
Mar
28
answered If y forms Pythagorean triples with two different x, can some other y also form Pythagorean triples with those two x?
Mar
28
comment Non existence of cyclic infinite linear algebraic groups
Defintely $\mathbf{G}_a$ and $\mathbf{G}_m$ do not have finitely generated subgroup as its $\mathbf{Q}$-points, for get cyclicity. Is there any clue in exponential mapping ?
Mar
27
answered Where in mathematics do these polynomials appear?
Mar
26
awarded  Necromancer
Mar
26
comment What is the name for the type of matrices?
Please add at least one $2\times 2$ example to help us.
Mar
26
comment Isometric embedding of SO(3) into an euclidean space
I see your objection. If we banish $\theta=0$ the remaining part should be topologically a non-monster, and can the whole thing be regarded as one-point compactification of that thing? Assuming there is a connection between minimal embedding dimensions of a manifold and its one-point compactification this might be useful. Is this approach worthwhile?
Mar
25
answered Structures that turn out to exhibit a symmetry even though their definition doesn't
Mar
25
comment Isometric embedding of SO(3) into an euclidean space
@ Ben: Not sure I understand. Why should it be $S^2$? For a unit vector $v\in \mathbf{R}^3$ and $\theta\in [0,2\pi)$ is not the 3d-rotation corresponding to the pair $(v,\theta)$ the same as that for $(-v,\theta)$? I guess it should be $\mathbf{RP}^2$.
Mar
25
answered Isometric embedding of SO(3) into an euclidean space