# All Questions

98,519 questions
161 views

### Generalizations of the “Curious Tiger” Polygon

I actually don't know, whether the polygon I describe here already has name, but let me explain the problem, that is solved by the polygon, with a little story: Imagine a flat terrain with bushes ...
111 views
+200

### Kazhdan-Lusztig equivalence for Lie super-algebras

Let $\mathfrak g$ be a semi-simple Lie algebra. Kazhdan and Lusztig studied the category of representations of the corresponding affine Lie algebra (the central extension of $\mathfrak g((t))$) which ...
63 views

263 views

### Adding a dedication to a paper

A paper of mine (relatively junior mathematician) was just accepted in a good journal, and I was considering adding a dedication to the memory of a mathematician in my area that passed away, and whose ...
36 views

### When does a collection of sets forming a geometric lattice give the flats of a matroid?

Say we have a matroid on a finite set $X$. The collection of its flats forms a geometric lattice under $\subseteq$, where the join is given by intersection. This question is about the converse to ...
84 views

### Conformally flat homogeneous spaces

Let's say we have a homogeneous space $H\backslash G$. Is it possible to tell whether this homogeneous space admits a conformally flat metric just from its group structure? I am particularly ...
224 views

### Write the algebra closure of $F_p$ as union of finite fields [closed]

This question follows Field theory by Steven Roman, Chapter 9, Exercise 20. Denote the algebraic closure of the finite field $F_q$ by $\Gamma(q)$, and let $a_n$ be any strictly increasing infinite ...
49 views

### Do we have criteria of strict localization of a Grothendieck category?

Let $\mathcal{C}$ be an abelian category and $\mathcal{S}$ be a full subcategory of $\mathcal{C}$. We call $\mathcal{S}$ a Serre subcategory of $\mathcal{C}$ if $\mathcal{S}$ is closed under ...
1k views

### are quotients by equivalence relations “better” than surjections?

This might be a load of old nonsense. I have always had it in my head that if $f:X\to Y$ is an injection, then $f$ has some sort of "canonical factorization" as a bijection $X\to f(X)$ followed by an ...
36 views

### Diffusion generators with gradient vector fields

Let $\mathcal{A}$ be a second order operator on an $n$-dimensional smooth manifold $M$, expressed in Hörmander form as $$\mathcal{A}=X_0+\frac{1}{2}\sum_i^kX_i^2,$$ where $X_0,X_1,...,X_k$ are ...
37 views

336 views

### Simple groups of the same order

I heard that there are no 3 nonisomorphic simple groups of the same order. Question: Is there an elementary proof of this? In case this is not the case, here a modified question: Question: Is ...
415 views

### Defining algebraic manifold without referring to schemes

Let $M$ be a complex manifold admitting an atlas with each chart biholomorphic to $\mathbb{C}^n$ and transition maps being rational functions. Is it true that there exists a smooth integral ...
63 views

81 views

### How to show mapping cones are homotopy cofibers

In a dg-category $\mathcal{C}$, the $n$-translation of an object $C$ is an object $C[n]$ representing the functor $${\rm Hom}(-,C)[n].$$ The cone of a closed morphism $f\colon C \to D$ of degree ...
63 views

### Prove or disprove the non colinearity of three points

Prove or disprove: Let $ABCD$ be a quadrilateral in Pasch Geometry for which the following holds $AB\cap CD=\{E\}$, $AC\cap BD=\{F\}$ and $AD\cap BC=\{G\}$. Then the points $E,F,G$ are not collinear. ...
150 views

### How to construct the espace étalé (space of sections) for an arbitrary category?

I want to consider the sheaf valued in an arbitrary category (not only of sets, groups, modules and so on) on a topological space, using the language of étalé space. In all references I am reading (...
This question is motivated by one of the problem set from this year's Putnam Examination. That is, Problem. Let $S_1, S_2, \dots, S_{2^n-1}$ be the nonempty subsets of $\{1,2,\dots,n\}$ in some ...
The Minkowski functional on a normed linear space $E$ is usually defined for convex (or sometimes even non convex) subsets $C$ of $E$ such that $0 \in \operatorname{int}(C)$. Is there any standard ...