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bio website people.bath.ac.uk/mdp33
location Bath, United Kingdom
age 25
visits member for 2 years, 8 months
seen 2 mins ago

Postgraduate student at the University of Bath, UK, studying geometry and representation theory. Currently thinking about cluster algebras and related objects.


Oct
7
comment $R/I$ is commutative iff $rs-sr \in I$
@spectraa Ok, that's better - now the other comments point out that this is essentially tautological.
Oct
7
comment $R/I$ is commutative iff $rs-sr \in I$
There are some problems with the question - firstly, the statement "$rs-sr$ is commutative for all $r,s\in R$" doesn't appear to depend on $I$, whereas the statement "$R/I$ is commutative" clearly does. Maybe one of $r$ or $s$ should be in $I$? Secondly, I don't know what you mean by "$rs-sr$ is commutative"; maybe that it is central (i.e. that $t(rs-sr)=(rs-sr)t$ for all $t$)? Or that it is zero?
Oct
7
comment Why are $\{0\}$ and $\{1\}$ open subsets of the discrete metric space $\{0,1\}$?
You should remind yourself of the definition of $B_S(x,r)$; the crucial thing to remember (which can be intuitively confusing) is that if $S=\{0,1\}$, then $B_S(x,r)$ contains far fewer points than $B_{\mathbb{R}}(x,r)$! Balls in $S$ don't look like open balls as you would usually imagine them.
Oct
6
answered Solving -2A - 2B = 2
Oct
6
revised Parametric equations of surfaces of revolution
edited body
Oct
3
comment Remark 3.1.3 from Introduction to Representation Theory from Pavel Etingof
The definition of the map is analogous to defining a linear map on a basis; a general element of the domain is (or if you prefer, "can be thought of as") a sum of elements of the form $g\otimes x$. The map $f$ has to be linear, so $f\colon(g_i\otimes x_i)_{i\in I}\mapsto\sum_{i\in I}g_i(x_i)$.
Oct
2
comment commutative ring with no zero divisors
OK - for completeness and future reference, because lots of people use lots of different definitions, it might be good to say this in the question, and to say whether or not an integral domain is required to have an identity.
Oct
2
comment commutative ring with no zero divisors
Does the definition of a ring in Gallian require a multiplicative identity? It seems this makes a difference.
Oct
2
revised commutative ring with no zero divisors
added 270 characters in body
Oct
2
comment commutative ring with no zero divisors
@CSA I should have guessed something like this would happen! Thanks for catching, I'll add a disclaimer.
Oct
1
comment Mathematical breakthroughs
You might have to say what you mean by "recent", bearing in mind that the influence of a theory (rather than a theorem) may take more time to become apparent.
Oct
1
answered commutative ring with no zero divisors
Sep
30
awarded  Explainer
Sep
30
comment Defining an isomorphism
I don't know what $U(8)$ is - you might want to explain a bit more. If you're asking whether it's ok to define a function on a finite set by specifying the image of each element individually (rather than 'giving a formula'), then the answer is yes.
Sep
30
comment Reflection in terms of simple reflections
I don't want to say no, but I think it's unlikely that some simple formula exists. There may be an algorithmic procedure, but the solution is not unique, so this would have to involve either arbitrary choices, or the input of a bit more information than just $\beta$. The expressions can get quite complicated - for example, you can see a choice of expression for the reflection in the longest root in each finite simple root system on page 15 of the following paper by Benkart-Kang-Oh-Park: arxiv.org/pdf/1108.1048v3.pdf.
Sep
30
comment A question regarding Yoneda's lemma.
A map $f\colon B\to C$ induces a map $f_A^*\colon\operatorname{Mor}(C,A)\to\operatorname{Mor}(B,A)$ defined by $f_A^*(u)=u\circ f$. The statement in the edit is that $i_B\circ f_A^*=f_{A'}^*\circ i_C$ for any $f\colon B\to C$ - this property is crucial for the statement you want to prove.
Sep
29
revised Solve a linear function
edited tags
Sep
26
revised By using De Moivre's Theorem, show that $\cos5\theta = 16\cos^5 \theta - 20 \cos^3 \theta + 5 \cos \theta$
edited title
Sep
26
reviewed Edit suggested edit on Showing that the direct product does not satisfy the universal property of the direct sum
Sep
26
revised Showing that the direct product does not satisfy the universal property of the direct sum
Fixed formatting, corrected flow, added category-theory tag for good measure