# All Questions

11 views

### normal groups of a nonabelian p-group

Let $G$ be a finite nonabelian $p$-group. For any $x\in G$ such that $x^{p}=1$, does there exist a normal subgroup $N$ of $G$ such that $x\not\in N$?
9 views

### Explicit representation for algrebra of smooth functions on a manifold

Suppose we have some smooth manifold $M$. Space of its smooth functions $C(M)$ is an algebra, and as far as I understand, it is $C^*$-algebra by trivial involution. Every $C^*$-algebra has a ...
10 views

### Generating $\mathfrak{so}(7)$

Short version: Let $V$ be a 7-dimensional linear space of (real) square matrices. Suppose further that $[V,V]$ (the linear space spanned $[X,Y]$, $X,Y\in V$) is isomorphic to $\mathfrak{so}(7)$. Can ...
16 views

### 4-D lattices and quaternion

It is easy to prove that there are only 2 extensions $\mathbb{Q}(a)$, with $|a|=1$, of $\mathbb{Q}$ where $\mathbb{Z}[a]$ becomes a lattice(discrete free abelian subgroup of rank 2) in the complex ...
6 views

### algorithms to solve convex problems

which algorithms are used to solve convex / SOCP problems? for instance, which numerical algorithm is implemented in Sedumi or cvxgen? interior-point methods, or something else? Thanks
23 views

### Extending the topology on a set to the group/vector space it generates

The multiplicative group $\Bbb Q^+$ can be viewed as a $\Bbb Z$-module. To see this, note that any rational can be decomposed into the form $2^{n_2} \cdot 3^{n_3} \cdot 5^{n_5} \cdot ...$ The tuple ...
28 views

### Relation between crystalline and perverse sheaves

Take $X$ to be a smooth complex projective algebraic variety. The Riemann-Hilbert correspondence gives an equivalence of categories between the category of perverse sheaves on $X$ and the category of ...
26 views

### Mathematical Definition of $n$-Brouillin Zone [duplicate]

I am having trouble finding a mathematical definition of the Brouillin zone beyond the first, which are basically the Voronoi cells or Wigner-Seitz cells. We could imagine the set of point closer to ...
22 views

### A certain measure on $C^{*}$algebras

Is there a reference who introduce the following measure on a $C^{*}$ algebra and investigate it from the view point of $C^{*}$ algebra or from the view point of ergodic theory?: Let $A$ be a $C^{*}$ ...
31 views

### Equivalence of questions regarding restrictions of pure states

In Davidson and Szarek's article "Local Operator Theory, Random Matrices and Banach Spaces" in the Handbook of the Geometry of Banach Spaces, the authors discuss the (now solved) Kadison-Singer ...
315 views

### Statements going against the grain of Riemann Hypothesis (R.H.)

Let $M(N) := \sum_{n=1}^N \mu(n)$ It is known that bounding $M(N)$ by $N^{1/2+\epsilon}$ implies R.H. A bound of $M(N)$ by $K\sqrt N$ for say $K\ge2$ is also sufficient. $K = 1$ is excluded as ...
21 views

### Solving for f given constraint involving f(x, y) and f(xy, y)

I am interested in a weighted version of the Catalan numbers. The generating function for this case, $$f(x, y) = \sum_s \sum_n f_{s n} x^s y^n$$ (where the $y^n$ term is the weight), obeys the ...
148 views

### Power sums of p-th roots of unity

The following question was asked by a colleague of mine. For any prime $p$ consider $$M_p:=\min_{z_1,\dots,z_p}\max_{j,k}\left|z_1^k+\dots+z_j^k\right|,$$ where $z_1,\dots,z_p$ are the complex $p$-th ...
80 views

### Spectral sequences to compute Hom's in derived category

Does anybody have a good reference that lists spectral sequences that may be used to compute Hom sets in derived categories (of coherent sheaves, say)?
37 views

### Explicit construction of a bielliptic curve

Let $C$ be a (projective smooth complex) curve such that $K_C=2(D+p)$, with $D+p$ defining a $g_7^2$; $p$ is a base point and $D$ defines a 2-to-1 map $\varphi:C\rightarrow E\subset\mathbb{P}^2$ onto ...
59 views

### Is there currently a known way to construct an injective mapping that transforms finite graphs into discrete geometric objects?

If there is such a mapping, it seems as though it could turn the graph isomorphism problem from a purely combinatorial problem to a discrete geometric one.
66 views

### In commutativity theorems in ring theory

Suppose that $R$ is a ring such that for any $x\in R$ there exists $1<n(x)\in \mathbb{N}$ such that $x^{n(x)}-x\in Z(R)$. Prove that $R$ is commutative or if it is not commutative, then the ideal ...
52 views

### What is know about maps between loop spaces of Spheres? - Reference request

What is know in general about the maps $\Omega^rS^n\rightarrow\Omega^sS^m$ between loop spaces of Spheres, or, perhaps to phrase it better, the groups $[\Omega^rS^n,\Omega^sS^m]$ for various values ...
24 views

It shall be an old story in PDE. I am looking for a sufficient condition of Dirichlet problem for the existence of the unique viscosity solution of the equation in the form of $$\inf_{a \in [-1,1]} \{... 0answers 43 views ### Stabilizers of pairs of ternary quadratic forms Let A,B be two ternary quadratic forms with real coefficients, given by symmetric matrices$$\displaystyle 2A = \begin{pmatrix} 2a_{11} & a_{12} & a_{13} \\ a_{12} & 2a_{22} & a_{23}...
42 views

There are many candidates of suspension operad in literature. Among them, $\Lambda= {\rm End}_{s\mathbb{K}}$ and $\Lambda'=\{s^{1-n}\mathbb{K}\otimes sgn_n\}_{n\geq 0}$ are typical ones. The oeprad ...
55 views

### Is the natural isomorphism $|FX_\bullet| \cong F|X_\bullet|$ lax symmetric monoidal?

Let $\mathcal{V_1}$ and $\mathcal{V_2}$ be cocomplete symmetric monoidal categories, each endowed with a cosimplicial object $\Delta^\bullet=\Delta^\bullet_{\mathcal{V}_i}:\Delta \to \mathcal{V}_i$. ...
153 views

### In what language do you think when doing mathemematics? [on hold]

Today, nearly all important papers are written in English. People whose mother tongue is not English nevertheless have to learn English if they want to be a mathematician. My question concerns these ...
32 views

### Compact Embeddings [on hold]

Put: $D=\{u\in L^{2}(\mathbb{R}^{2})| N=(x\frac{d}{dy}- y \frac{d}{dx})u\in L^{2}(\mathbb{R}^{2}) \}$ Why $D \hookrightarrow L^{2}(\mathbb{R}^{n})$ with compact injection? Thank you in advance.
137 views

### Reducibility of determinantal hypersurfaces

I have a determinantal hypersurface defined by $\det(A)=0$, with $a_{ij}$ homogeneous polynomial of fixed degree $d$ in $n$ variables. $A$ is not diagonal. How can I find out whether the hypersurface ...
30 views