Reputation
5,176
Next privilege 10,000 Rep.
Access moderator tools
Badges
2 14 35
Newest
 Revival
Impact
~71k people reached

11h
comment Acting algebraically
Is G an algebraic group? Is V a variety?
Jul
1
comment Relations between $R^fG$ and either $\mathbb{C}^fG$ or $\mathbb{Z}^fG$.
What do $\bar f$ and $\tilde f$ really mean? The obvious interpretation of $f$ is as (the class of) a map $G \times G \to R^\times$ -- how does this give a map $G \times G \to \{\pm 1\}$?
Jun
25
comment Is there a short symbol that denotes integration?
People write $f^{(r)}$ for $f$ differentiated $r>0$ times (no indication of which variable you differentiate with respect to). You could just extend this to negative $r$, though it is definitely not standard notation.
Jun
24
comment How to determine non trivial homomorphisms
There is no algorithm that will solve all of these problems, so the method you should use depends entirely on the groups or rings involved.
Jun
24
comment How to express a=8 versus b=4?
Do you want to say $a$ is larger than $b$ by 4? This means $a-b=4$, so 9 is larger than 5 by 4. You can also say 9 is 4 larger than 5, or 9 is larger by 4 than 5.
Jun
18
comment Where is Cauchy's wrong proof?
Salut Shadock, I have copied the text exactly as Cauchy wrote it (though I agree differens must be a mistake). It is from 1821, perhaps things have changed...
Jun
18
revised Where is Cauchy's wrong proof?
added 654 characters in body
Jun
16
comment What is $\lim_{n\to \infty} \sqrt{x_n+2}$?
Try proving by induction that $x_n \leq 2$ for all $n$.
Jun
12
comment If $\mathcal{L}$ is a minimal left ideal of an algebra $\mathcal{A}$, then $\mathcal{A}l=\mathcal{L}$ for all $l\in \mathcal{L}$?
There's no associativity assumption in the OP's definition of algebra.
Jun
11
comment What is the flaw in my thinking for the graph of this function?
Thanks Anthony.
Jun
11
comment What is the flaw in my thinking for the graph of this function?
This animation is excellent, how did you make it?
Jun
6
comment Example of a finite dimensional algebra over $C$ with a simple module of dimension $2013$
Try showing that the height n column vectors are a simple module for the nxn matrix algebra.
Jun
6
revised How can AC be listed as a single voltage
rolled back to a previous revision
Jun
4
comment Humphreys Introduction to Lie Algebras - Conjugate Borel subalgebras sl(2,F)
$H+L_\alpha$ won't be big enough to be a Borel for larger Lie algebras, but yes I think this is how it works for $\mathfrak{sl}(2,\mathbb{F})$.
Jun
3
comment New Horizons at Pluto
codingthematrix.com is good for linear algebra applications in computer science, including image manipulation
Jun
3
comment Humphreys Introduction to Lie Algebras - Conjugate Borel subalgebras sl(2,F)
They're not the only Borels (e.g. take one of them and conjugate it by some invertible matrix and you usually get something different), but remember that in the proof of your last case you conjugate $B \cap A$ to $\mathbb{F}h$ so you are no longer dealing with arbitrary $B$. Possibly the only Borels of sl2 containing this subspace are the upper and lower triangular ones.
Jun
3
reviewed Approve $sin$ inequality
Jun
2
revised Humphreys Introduction to Lie Algebras - Conjugate Borel subalgebras sl(2,F)
added 250 characters in body
Jun
2
comment Humphreys Introduction to Lie Algebras - Conjugate Borel subalgebras sl(2,F)
There's clearly a problem in your final case 2, since you could have $B$ the upper triangular Borel and $A$ the lower triangular. Can you explain why the general proof then forces $x \in A$?
May
31
comment Very tentative proof of Beal's Conjecture?
$\sqrt{x+y} \neq \sqrt{x}+\sqrt{y}!$