اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدLow degree cohomologies of congruence groups
226
0
0.0
(
0
)
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
We prove the vanishing of certain low degree cohomologies of some induced representations. As an application, we determine certain low degree cohomologies of congruence groups.
قيم البحث
اقرأ أيضاً
In this paper, first we give the notion of a representation of a relative Rota-Baxter Lie algebra and introduce the cohomologies of a relative Rota-Baxter Lie algebra with coefficients in a representation. Then we classify abelian extensions of relat
ive Rota-Baxter Lie algebras using the second cohomology group, and classify skeletal relative Rota-Baxter Lie 2-algebras using the third cohomology group as applications. At last, using the established general framework of representations and cohomologies of relative Rota-Baxter Lie algebras, we give the notion of representations of Rota-Baxter Lie algebras, which is consistent with representations of Rota-Baxter associative algebras in the literature, and introduce the cohomologies of Rota-Baxter Lie algebras with coefficients in a representation. Applications are also given to classify abelian extensions of Rota-Baxter Lie algebras and skeletal Rota-Baxter Lie 2-algebras.
We enumerate all the principal congruence link complements in $S^3$, there by answering a question of W. Thurston. Related articles: Technical Report: All Principal Congruence Link Groups (arXiv:1902.04722), All Known Principal Congruence Links (arXiv:1902.04426).
Two matrix vector spaces $V,Wsubset mathbb C^{ntimes n}$ are said to be equivalent if $SVR=W$ for some nonsingular $S$ and $R$. These spaces are congruent if $R=S^T$. We prove that if all matrices in $V$ and $W$ are symmetric, or all matrices in $V$
and $W$ are skew-symmetric, then $V$ and $W$ are congruent if and only if they are equivalent. Let $F: Utimesdotstimes Uto V$ and $G: Utimesdotstimes Uto V$ be symmetric or skew-symmetric $k$-linear maps over $mathbb C$. If there exists a set of linear bijections $varphi_1,dots,varphi_k:Uto U$ and $psi:Vto V$ that transforms $F$ to $G$, then there exists such a set with $varphi_1=dots=varphi_k$.
The congruence subgroup problem for a finitely generated group $Gamma$ asks whether $widehat{Autleft(Gammaright)}to Aut(hat{Gamma})$ is injective, or more generally, what is its kernel $Cleft(Gammaright)$? Here $hat{X}$ denotes the profinite completi
on of $X$. In this paper we first give two new short proofs of two known results (for $Gamma=F_{2}$ and $Phi_{2}$) and a new result for $Gamma=Phi_{3}$: 1. $Cleft(F_{2}right)=left{ eright}$ when $F_{2}$ is the free group on two generators. 2. $Cleft(Phi_{2}right)=hat{F}_{omega}$ when $Phi_{n}$ is the free metabelian group on $n$ generators, and $hat{F}_{omega}$ is the free profinite group on $aleph_{0}$ generators. 3. $Cleft(Phi_{3}right)$ contains $hat{F}_{omega}$. Results 2. and 3. should be contrasted with an upcoming result of the first author showing that $Cleft(Phi_{n}right)$ is abelian for $ngeq4$.
We study general properties of the dessins denfants associated with the Hecke congruence subgroups $Gamma_0(N)$ of the modular group $mathrm{PSL}_2(mathbb{R})$. The definition of the $Gamma_0(N)$ as the stabilisers of couples of projective lattices i
n a two-dimensional vector space gives an interpretation of the quotient set $Gamma_0(N)backslashmathrm{PSL}_2(mathbb{R})$ as the projective lattices $N$-hyperdistant from a reference one, and hence as the projective line over the ring $mathbb{Z}/Nmathbb{Z}$. The natural action of $mathrm{PSL}_2(mathbb{R})$ on the lattices defines a dessin denfant structure, allowing for a combinatorial approach to features of the classical modular curves, such as the torsion points and the cusps. We tabulate the dessins denfants associated with the $15$ Hecke congruence subgroups of genus zero, which arise in Moonshine for the Monster sporadic group.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
