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bio website people.bath.ac.uk/mdp33
location Bath, United Kingdom
age 24
visits member for 2 years, 2 months
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Postgraduate student at the University of Bath, UK, studying geometry and representation theory. Currently thinking about cluster algebras and related objects.


Jan
21
comment Relation between direct sum and tensor product
Your question might need additional clarity - every object is the direct sum of just itself. In the Lie group setting, at least when the group is simple, the category of representations is Krull-Schmidt, so every object is a direct sum of indecomposables, rather than this being something special about tensor products. Same for the category of finite dimensional vector spaces (although of course what you have written is not in general the decomposition into a sum of indecomposables).
Jan
21
answered Is $k[x,y]/(x,y) \cong k$?
Jan
21
answered Notation for quotient ring
Jan
17
comment Is the notation $X²$ an abuse of language in a polynomial ring.
Oh, right. That's not what is happening - firstly, you only have one indeterminate, and secondly, there is a relationship between $X$ and $X^2$ that you want to capture, namely that $X\times X=X^2$. If you write a completely new variable instead of $X^2$, the notation doesn't make it clear that this relationship should hold.
Jan
17
comment Is the notation $X²$ an abuse of language in a polynomial ring.
What do you mean by $X_2$?
Jan
17
revised What does this symbol “$\gg$” mean
deleted 81 characters in body; edited title
Jan
16
answered Consequences of Schur's Lemma
Jan
16
revised Consequences of Schur's Lemma
added 33 characters in body
Jan
16
comment X-infinite, consider zariski topology.
What is your definition of the Zariski topology? (I'm aware of two different ones, although one is less common).
Jan
16
answered Help with proof that Zp is an Integral Domain iff p is prime.
Jan
16
comment Why can infinite series be summed different ways to get different results?
@5xum Certainly - I think both interpretations say something interesting.
Jan
16
comment Why can infinite series be summed different ways to get different results?
While that's a nice way of thinking, I think a better way of interpreting the failure of rearrangement in the non-absolutely convergent case is as a reminder that the order of the series is a necessary part of the data. After all, if you change the order, you get a different sequence of partial sums, so in some sense it shouldn't be surprising that it might have a different limit.
Jan
16
answered Why can infinite series be summed different ways to get different results?
Jan
15
reviewed Approve suggested edit on Universal Generalization properties
Jan
15
reviewed Approve suggested edit on How to solve the following pair of equation.
Jan
15
reviewed Reject suggested edit on Division Rings and Division Algebras
Jan
15
reviewed Approve suggested edit on How to correctly do a division using a slash?
Nov
25
reviewed Close Prove by induction that $a-b|a^n-b^n$
Nov
25
comment Ideals in a real/complex number field?
A related result to those in the answers is that every homomorphism of fields is injective (assuming we make the usual requirement that $\varphi(1)\ne\varphi(0)$ when $\varphi$ is a homomorphism of fields - else the zero map would be the one exception).
Nov
22
comment What is the most mathematical flag?
Was I really the only person to think of a chain of subspaces of a vector space? ;) en.wikipedia.org/wiki/Flag_(linear_algebra)