7,976 reputation
1642
bio website people.bath.ac.uk/mdp33
location Bath, United Kingdom
age 24
visits member for 2 years, 5 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.


Sep
4
comment More Bases for Strong Induction - Supersedes Weak Induction?
The link you gave doesn't say that you need more base cases in general, this just happens in the example. But this could happen with either form of induction.
Sep
4
reviewed Reopen How to prove that $2+2 = 2*2 = 2^2 \cdots= 4$
Sep
4
comment Variation of the Principle of Mathematical Induction
Or you could define $r_k=0$ when $k<0$.
Sep
4
comment Best Books to learn Proof-Based Linear Algebra and Matrices
While I don't think it's a duplicate, you may find the answers to the following question useful: math.stackexchange.com/questions/4335/…
Sep
3
reviewed No Action Needed Mean response in linear regression
Sep
3
comment Subset of $\mathbb{R}^3$ with an element of finite order in its fundamental group
Unfortunately, yes - $\mathbb{R}P^2$ does not embed in $\mathbb{R}^3$ (but it does embed into $\mathbb{R}^4$).
Sep
2
comment A category's quotient category of isomorphism types
The first author has some implicit assumptions about what properties the category on the isomorphism classes should have; one could define a category whose objects are the isomorphism classes of objects of $\mathcal{C}$, by giving each object its identity morphism and then stopping. The result would not have a particularly interesting or useful relationship to $\mathcal{C}$ though. So one possibility is that whatever conditions the first author thinks the resulting category should meet are not met by the category defined by the second author.
Sep
2
revised orbits of group action on product space and orbits of stablizer are in 1-1 correspondence?
added 39 characters in body
Sep
2
revised Show that the mapping $x\rightarrow x^{-1}$ of $G$ onto $G$ is an isomorphism iff $G$ is abelian
edited title
Sep
2
reviewed Looks OK $2d^2=n^2$ implies that $n$ is multiple of 2
Sep
2
reviewed Looks OK Prove that if $n > 4$ is composite $n|(n-1)!$
Sep
2
revised Show that $R/\langle a_i\rangle$ is torsion
added 105 characters in body; edited title
Sep
2
reviewed No Action Needed Concavity: composition of multivariate functions
Aug
30
comment Prove that $S$ is a sphere.
@Arthur A single point (and maybe even the empty set) could be thought of as very degenerate spheres, or you could add the extra conditions you suggest. A hemisphere wouldn't satisfy the second condition, as some planes would intersect it in a semicircle.
Aug
29
comment When are infinite dimensional path algebras hereditary
If an associative algebra $A$ is finite dimensional, basic, connected and defined over an algebraically closed field $K$, then $A$ is hereditary if and only if it is isomorphic to the path algebra of a finite, connected and acyclic quiver (see Thm. VII.1.7 of Assem-Simson-Skowroński). However, this still leaves the more interesting cases of your question unanswered...
Aug
29
revised Norm of a mapping
added 6 characters in body
Aug
29
comment Does representation theory exists without Groups?
Instead of removing structure, you can add more - there is a huge amount of representation theory developed for rings and algebras (both associative and some non-associative).
Aug
29
comment For $f : V \to V$ a nilpotent endomorphism, with minimal polynomial $x^m$. Why $f^{m-1}(V) \subset ker(f)$?
Pick some $v\in V$. What is $f(f^{m-1}(v))$?
Aug
29
comment Question about the definition of cluster algebras.
@AndreasBlass Corrected - I usually have $\mathbb{C}$ in place of $\mathbb{Q}$, which is where that came from.
Aug
29
revised Question about the definition of cluster algebras.
deleted 140 characters in body