# All Questions

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### Does an element in the center of universal enveloping algebra becomes a scalar in irreducible representations?

I'm asking a question about Lie group representation. Let $G$ be a Lie group, not necessarily connected. Let $\Omega$ be an element in the center of the universal enveloping algebra $U(\mathfrak{g})$ ...
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### Pointfree probability theory

I must confess I hardly know anything about probability theory. Still, I'm interested in the following: Much like pointfree topology, where one basically replaces topological spaces by their locales ...
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### A finite group with O_{p}(G)=1

Let $G$ be a finite group of order $p(p^2-1)/2$, where $p$ is prime number. If $O_{p}(G)=1$, then what is the number of Sylow $p$-subgroups G?
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### What characteristic of a graph depend on the vertex labeling?

Different labeling on a graph produces class of isomorphic graphs. Two isomorphic graphs possess similar characteristic such as connectivity, degree distribution of vertices, equality of spectrum and ...
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### Any polynomial-time algorithm for hypergraph bisection?

I work with hypergraph partitioning. I want to divide a complete weighted hypergraph into 2 parts using cut-net metric, a sum of all edges cut, and connectivity metric. Is there a polynomial-time ...
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### Is an irreducible ideal in $R$ also irreducible in $R[x]$?

Let $R$ be a commutative Noetherian ring and $I\subset R$ an ideal that is irreducible in the sense that if $I = J_1 \cap J_2$, then $I=J_1$ or $I=J_2$. Is (the ideal generated by) $I$ irreducible in ...
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### Vanishing natural transformation and strong generator

Let $X$ be a smooth projective variety (over the field of complex numbers). Let $T$ be strong generator of $D^b(X)$ : this means that every object in $D^b(X)$ can be obtained in a given finite number ...
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### Non-standard numbers and exponential form of Zeta function

Basic idea For a long time I was looking for a numerical system that would allow to compare infinite sets. In contrast to Cantor's approach that empathizes the possibility of on-to-one correspondence ...
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### Properties of Coefficients of Order Polynomials

I am working on a problem involving determining the order polynomial $\Omega_P(k)$ of a partial order $P$, which counts the number of order-preserving transformations/maps from $P$ to the $k$-chain ...
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### A finite field $0$-free restrictive sumset problem

Fix $m\in\Bbb N$. Let $\Bbb F_2^{\big\lceil\log^d m\big\rceil}$ be $\Big\lceil\log^dm\Big\rceil$-dimensional vector space over $\Bbb F_2$. What is minimum $d$ (if it exists - need sufficient ...
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### Is there a non-smooth algebraic group scheme in char $p$, all of whose defining relations have degree less than $p$?

Let $k$ be an algebraically closed field of characteristic $p>0$. All the examples of non-smooth algebraic group schemes over $k$ that I have seen (apart from "artificial" examples; see below) have ...
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### Examples of common false beliefs in mathematics

The first thing to say is that this is not the same as the question about interesting mathematical mistakes. I am interested about the type of false beliefs that many intelligent people have while ...
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### coproduct of the homology of iterated loop space on spheres

Let $\Omega^{n+1}S^{n+1}$ be the base-pointed $(n+1)$-iterated loop space on the $(n+1)$-sphere. In the paper The homology of $\mathcal{C}_{n+1}$-spaces, $n\geq 0$, F. Cohen, Lecture notes in ...
First we talk about dg-algebras. According to this n-lab page, we write $dgAlg$ for the category of cochain dg-algebras in non-negative degree over a field $k$ of characteristic $0$. Write ...