首页/论文/math/9801100

arXiv math/98011001998-01-21math.GRmath.KT

Z[t]和Z[t，t^{-1}]上线性群的相对完备化

Relative completions of linear groups over Z[t] and Z[t,t^{-1}]

Kevin P. Knudson

备注：: 13 pages

阅读 PDF ↗

arXiv 页面 ↗HTML 原文 ↗

摘要英文摘要相关论文

摘要：

我们计算了群SL_n（Z[t]）和SL_n（Z[t，t^{-1}]）相对于SL_n（Q）的明显同态的完备化，这是经典Malcev完备化的推广.我们还对这些群的有理二上同调作了部分计算。

英文摘要：

We compute the completion of the groups SL_n(Z[t]) and SL_n(Z[t,t^{-1}]) relative to the obvious homomorphisms to SL_n(Q); this is a generalization of the classical Malcev completion. We also make partial computations of the rational second cohomology of these groups.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

阅读原文

阅读 PDF ↗

arXiv 页面 ↗HTML 原文 ↗

本文内容

摘要英文摘要相关论文

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

继续探索

相关论文

局部环上线性群的相对完备化与上同调

Relative completions and the cohomology of linear groups over local rings

本文研究了域$k$上约化代数群中相对于Zebraki稠密表示的群的完备化问题。特征零情况以前由R. Hain;我们将他的结果推广到任意特征。主要应用是研究群的上同调，如$SL_n(k[[T]])$。

2001-04-02math.ATmath.GRmath.KT

相对双曲的实际上特殊群的profinite完备化

The profinite completion of relatively hyperbolic virtually special groups

本文利用profinite完备化刻画toral相对双曲的实际上特殊群，并证明其完备化子群的Tits二择一与有限生成pro-p子群结构，结果应用于双曲算术流形及同余核。

2025-03-15math.GR

C*-simplicity of relative profinite completions of generalized Baumslag-Solitar groups

Suzuki recently gave constructions of non-discrete examples of locally compact C*-simple groups and Raum showed C*-simplicity of the relative profinite completions of the Baumslag-Solitar groups by using Suzuki's results. We extend this result to some fundamental groups of graphs of groups called generalized Baumslag-Solitar groups. In this article, we focus on some sufficient condition to show that these locally compact groups are C*-simple and that KMS-weights of these reduced group C*-algebras are unique. This condition is an analogue of the Powers averaging property of discrete groups and …

2022-01-27math.GRmath.OA

相对双曲群的极限与Lyndon完备化

Limits of relatively hyperbolic groups and Lyndon's completions

在本文中，我们描述了有限生成群$H$等价于一个给定的挠自由相对双曲群$G$与自由交换抛物（在语言中，常数从$G$）。事实证明，在自由群的情况下，群$H$嵌入到群$G$的林登完备化$G^{\mathbb{Z}[t]}$中，或者等价地，$H$嵌入到通过中心化器的许多扩张从$G$获得的群中。相反，包含$G$的$G^{\mathbb{Z}[t]}$的每个子群普遍等价于$G$。由于普遍等价于$G$的有限生成群恰好是由$G$区分的有限生成群，所以上述结果给出了由$G$区分的有限生成群的描述。

2011-11-02math.GR

关于Schlichting完成的同调性质

On homological properties of the Schlichting completion

Karlsruhe Institute of Technology（卡尔斯鲁厄理工学院）

本文研究了Schlichting完成的同调性质，探讨了群与子群的有限性属性转移，并证明Neretin群的持续同调在正度数上为零。

2024-07-18math.GR

Baumslag-Solitar群、相对profinite完备化与测度等价刚性

Baumslag-Solitar groups, relative profinite completions and measure equivalence rigidity

本文为保测度等价关系的非周期包含引入代数不变量，借此证明了非顺从Baumslag-Solitar群直积自由pmp作用的稳定轨道等价刚性，并完成了其相对profinite完备化直积的完全分类。

2015-02-27math.DSmath.GR

更多相关论文收起更多论文

Relative cohomology theory for profinite groups

In this paper we define and develop the theory of the cohomology of a profinite group relative to a collection of closed subgroups. Having made the relevant definitions we establish a robust theory of cup products and use this theory to define profinite Poincaré duality pairs. We use the theory of groups acting on profinite trees to give Mayer-Vietoris sequences, and apply this to give results concerning decompositions of 3-manifold groups. Finally we discuss the relationship between discrete duality pairs and profinite duality pairs, culminating in the result that profinite completion of the …

2017-10-02math.GRmath.GTmath.KT

群代数的非阿基米德完备化的同调代数

Homological algebra for nonarchimedean completions of group algebras

本文证明了群代数到其 dagger 完备化的典范态射是等上同调态射，从而将完备化代数的同调性质归约为较简单的群代数，并应用于 Hochschild 与循环同调计算。

2023-11-17math.FAmath.GRmath.KT

Geometric equivalence of $π$-torsion free nilpotent groups

In this paper we study the property of geometric equivalence of groups introduced by B. Plotkin \cite{P1, P2}. Sufficient and necessary conditions are presented for a $π$-torsion-free nilpotent group to be geometrically equivalent to its $π$-completion. We prove that a relatively free nilpotent $π$-torsion-free group and its $π$-completion define the same quasi-variety. Examples of $π$-torsion-free nilpotent groups that are geometrically equivalent to their $π$-completions are given.

2018-02-04math.AGmath.GR

Limit groups over coherent right-angled Artin groups are cyclic subgroup separable

We prove that cyclic subgroup separability is preserved under exponential completion for groups that belong to a class that includes all coherent RAAGs and toral relatively hyperbolic groups; we do so by exploiting the structure of these completions as iterated free products with commuting subgroups. From this we deduce that the cyclic subgroups of limit groups over coherent RAAGs are separable, answering a question of Casals-Ruiz, Duncan and Kazachov. We also discuss relations between free products with commuting subgroups and the word problem, and recover the fact that limit groups over cohe…

2021-01-25math.GR

The additive completion of the biset category

Let $R$ be a commutative unital ring. We construct a category $\mathcal{C}_R$ of fractions $X/G$, where $G$ is a finite group and $X$ is a finite $G$-set, and with morphisms given by $R$-linear combinations of spans of bisets. This category is an additive, symmetric monoidal and self-dual category, with a Krull-Schmidt decomposition for objects. We show that $\mathcal{C}_R$ is equivalent to the additive completion of the biset category and that the category of biset functors over $R$ is equivalent to the category of $R$-linear functors from $\mathcal{C}_R$ to $R$-Mod. We also show that the res…

2019-09-30math.CTmath.GRmath.RT

有限完备化的平凡性问题

The triviality problem for profinite completions

本文证明有限呈示群是否具有非平凡有限商不可判定，并将结果推广到非正曲率方形复形基本群及双曲群的多种性质。

2015-01-07math.GRmath.GT